Affected by the Federal Reserve's interest rate hike and the downward pressure on the domestic economy,the phenomenon of default is still prominent.The credit risk of the listed companies has become a growing conc...Affected by the Federal Reserve's interest rate hike and the downward pressure on the domestic economy,the phenomenon of default is still prominent.The credit risk of the listed companies has become a growing concern of the community.In this paper we present a novel credit risk measurement method based on a dimensional reduation technique.The method first extracts the risk measure indexes from the basal financial data via dimensional reduation by using deep belief network(DBN),exploratory factor analysis(EFA)and confirmatory factor analysis(CFA)in turn.And then the credit risk is measured by a systemic structural equation model(SEM)and logistic distribution.To validate the proposed method,we employ the financial data of the listed companies from Q12019 to Q22022.The empirical results show its effectiveness on statistical evaluation,assessment on testing samples and credit risk forecasting.展开更多
In this paper, we focus on anticipated backward stochastic Volterra integral equations(ABSVIEs) with jumps. We solve the problem of the well-posedness of so-called M-solutions to this class of equation, and analytical...In this paper, we focus on anticipated backward stochastic Volterra integral equations(ABSVIEs) with jumps. We solve the problem of the well-posedness of so-called M-solutions to this class of equation, and analytically derive a comparison theorem for them and for the continuous equilibrium consumption process. These continuous equilibrium consumption processes can be described by the solutions to this class of ABSVIE with jumps.Motivated by this, a class of dynamic risk measures induced by ABSVIEs with jumps are discussed.展开更多
Deep foundation pit excavation is a basic and key step involved in modern building construction.In order to ensure the construction quality and safety of deep foundation pits,this paper takes a project as an example t...Deep foundation pit excavation is a basic and key step involved in modern building construction.In order to ensure the construction quality and safety of deep foundation pits,this paper takes a project as an example to analyze deep foundation pit excavation technology,including the nature of this construction project,the main technical measures in the construction of deep foundation pit,and the analysis of the safety risk prevention and control measures.The purpose of this analysis is to provide scientific reference for the construction quality and safety of deep foundation pits.展开更多
This study explored the effects of ambiguity on the calculation of Value-at-Risk(VaR)using a mathematical model based on the theory of Choquet-Brownian processes.It was found that while a moderate degree of ambiguity ...This study explored the effects of ambiguity on the calculation of Value-at-Risk(VaR)using a mathematical model based on the theory of Choquet-Brownian processes.It was found that while a moderate degree of ambiguity aversion yields a higher value for VaR and Expected Shortfall(ES),the result can be reversed in a deeply ambiguous environment.Additionally,some sufficient conditions are provided for the preservation of this effect under various forms of risk aggregation.This study offers a new perspective to full awareness on capital requirement calculation as requested by international regulation.展开更多
This study considers the risk management of insurance policies in line with the implementation of the new International Financial Reporting Standards 17.It applies the paid-incurred chain method to model the future un...This study considers the risk management of insurance policies in line with the implementation of the new International Financial Reporting Standards 17.It applies the paid-incurred chain method to model the future unpaid losses by combining the information channels of both the incurred claims and paid losses.We propose the recovery of the empirical distribution of the outstanding claims liabilities associated with a group of contracts via moment-based density approximation.We determine the risk measures and adjustments that are compliant with the new standard using the Monte–Carlo simulation method and approximated distributions.The historical data on the aggregate Ontario automobile insurance claims over a 15-year period are analyzed to examine the appropriateness and accuracy of our approach.展开更多
This paper presents explicit formulae giving tight upper and lower bounds on the expectations of alpha-unimodal random variables having a known range and given set of moments. Such bounds can be useful in ordering of ...This paper presents explicit formulae giving tight upper and lower bounds on the expectations of alpha-unimodal random variables having a known range and given set of moments. Such bounds can be useful in ordering of random variables in terms of risk and in PERT analysis where there is only incomplete stochastic information concerning the variables under investigation. Explicit closed form solutions are also given involving alpha-unimodal random variables having a known mean for two particularly important measures of risk—the squared distance or variance, and the absolute deviation. In addition, optimal tight bounds are given for the probability of ruin in the collective risk model when the severity distribution has an alpha-unimodal distribution with known moments.展开更多
Reinsurance is an effective risk management tool for insurers to stabilize their profitability. In a typical reinsurance treaty, an insurer cedes part of the loss to a reinsurer. As the insurer faces an increasing num...Reinsurance is an effective risk management tool for insurers to stabilize their profitability. In a typical reinsurance treaty, an insurer cedes part of the loss to a reinsurer. As the insurer faces an increasing number of total losses in the insurance market, the insurer might expect the reinsurer to bear an increasing proportion of the total loss, that is the insurer might expect the reinsurer to pay an increasing proportion of the total claim amount when he faces an increasing number of total claims in the insurance market. Motivated by this, we study the optimal reinsurance problem under the Vajda condition. To prevent moral hazard and reflect the spirit of reinsurance, we assume that the retained loss function is increasing and the ceded loss function satisfies the Vajda condition. We derive the explicit expression of the optimal reinsurance under the TVaR risk measure and TVaR premium principle from the perspective of both an insurer and a reinsurer. Our results show that the explicit expression of the optimal reinsurance is in the form of two or three interconnected line segments. Under an additional mild constraint, we get the optimal parameters and find the optimal reinsurance strategy is full reinsurance, no reinsurance, stop loss reinsurance, or quota-share reinsurance. Finally, we gave an example to analyze the impact of the weighting factor on optimal reinsurance.展开更多
Tail risk is a classic topic in stressed portfolio optimization to treat unprecedented risks,while the traditional mean–variance approach may fail to perform well.This study proposes an innovative semiparametric meth...Tail risk is a classic topic in stressed portfolio optimization to treat unprecedented risks,while the traditional mean–variance approach may fail to perform well.This study proposes an innovative semiparametric method consisting of two modeling components:the nonparametric estimation and copula method for each marginal distribution of the portfolio and their joint distribution,respectively.We then focus on the optimal weights of the stressed portfolio and its optimal scale beyond the Gaussian restriction.Empirical studies include statistical estimation for the semiparametric method,risk measure minimization for optimal weights,and value measure maximization for the optimal scale to enlarge the investment.From the outputs of short-term and long-term data analysis,optimal stressed portfolios demonstrate the advantages of model flexibility to account for tail risk over the traditional mean–variance method.展开更多
The paper presents the properties of an alternative method,which measures market risk over time-horizon exceeding one day:Mark to market value at risk(MMVaR).Relying on the minimal returns during the time interval,thi...The paper presents the properties of an alternative method,which measures market risk over time-horizon exceeding one day:Mark to market value at risk(MMVaR).Relying on the minimal returns during the time interval,this method not only considers the non-normality of data and information about sample size,but also meets the requirement of increasing the minimal capital ratio in BaselⅢ,basically.The authors theoretically prove the translation invariance,monotonicity and subadditivity of MMVaR as a risk measure under some conditions,and study its finite sample properties through Monte Carlo simulations.The empirical analysis shows that MMVaR can measure multi-period risk accurately.展开更多
We study mean-field BSDEs with jumps and a generalized mean-field operator that can capture higher-order interactions.We interpret the BSDE solution as a dynamic risk measure for a representative bank whose risk attit...We study mean-field BSDEs with jumps and a generalized mean-field operator that can capture higher-order interactions.We interpret the BSDE solution as a dynamic risk measure for a representative bank whose risk attitude is influenced by the system.This influence can come in a wide class of choices,including the average system state or average intensity of system interactions.Using Fenchel−Legendre transforms,our main result is a dual representation for the expectation of the risk measure in the convex case.In particular,we exhibit its dependence on the mean-field operator.展开更多
G-VaR,which is a type of worst-case value-at-risk(VaR),is defined as measuring risk incorporating model uncertainty.Compared with most extant notions of worst-case VaR,G-VaR can be computed using an explicit formula,a...G-VaR,which is a type of worst-case value-at-risk(VaR),is defined as measuring risk incorporating model uncertainty.Compared with most extant notions of worst-case VaR,G-VaR can be computed using an explicit formula,and can be applied to large portfolios of several hundred dimensions with low computational cost.We also apply G-VaR to robust portfolio optimization,thereby providing a tractable means to facilitate optimal allocations under the condition of market ambiguity.展开更多
In the context of multivariate regular variation,the authors establish the first-order asymptotics of the spectral risk measure of portfolio loss.Furthermore,by the notion of second-order regular variation,the second-...In the context of multivariate regular variation,the authors establish the first-order asymptotics of the spectral risk measure of portfolio loss.Furthermore,by the notion of second-order regular variation,the second-order asymptotics of the spectral risk measure of portfolio loss is also presented.In order to illustrate the derived results,a numerical example with Monte Carlo simulation is carried out.展开更多
Reinsurance is an effective way for an insurance company to control its risk.How to design an optimal reinsurance contract is not only a key topic in actuarial science,but also an interesting research question in math...Reinsurance is an effective way for an insurance company to control its risk.How to design an optimal reinsurance contract is not only a key topic in actuarial science,but also an interesting research question in mathematics and statistics.Optimal reinsurance design problems can be proposed from different perspectives.Risk measures as tools of quantitative risk management have been extensively used in insurance and finance.Optimal reinsurance designs based on risk measures have been widely studied in the literature of insurance and become an active research topic.Different research approaches have been developed and many interesting results have been obtained in this area.These approaches and results have potential applications in future research.In this article,we review the recent advances in optimal reinsurance designs based on risk measures in static models and discuss some interesting problems on this topic for future research.展开更多
Natural events such as floods and landslides can have severe consequences.The risks are expected to increase,both as a consequence of climate change and due to increased vulnerabilities,especially in urban areas.Altho...Natural events such as floods and landslides can have severe consequences.The risks are expected to increase,both as a consequence of climate change and due to increased vulnerabilities,especially in urban areas.Although preventive measures are often cost-effective,some measures are beneficial to certain values,while some may have negative impacts on other values.The aim of the study presented here was to investigate two frameworks used for assessing the effectiveness and sustainability of physical and nonphysical flood and landslide risk reduction measures.The study is based on literature,available information from authorities and municipalities,expert knowledge and experience,and stakeholder views and values.The results indicate that the risks for suboptimization or maladaptation are reduced if many aspects are included and a broad spectrum of stakeholders are involved.The sustamability assessment tools applied here can contribute to a more transparent and sustainable risk management process by assessing strategies and interventions with respect to both short- and long-term perspectives,including local impacts and wider environmental impacts caused by climate change,for example.The tools can also cover social and economic aspects.The assessment tools provide checklists that can support decision processes,thus allowing for more transparent decisions.展开更多
This paper proposes a new approach for stock efficiency evaluation based on multiple risk measures. A derived programming model with quadratic constraints is developed based on the envelopment form of data envelopment...This paper proposes a new approach for stock efficiency evaluation based on multiple risk measures. A derived programming model with quadratic constraints is developed based on the envelopment form of data envelopment analysis(DEA). The derived model serves as an input-oriented DEA model by minimizing inputs such as multiple risk measures. In addition, the Russell input measure is introduced and the corresponding efficiency results are evaluated. The findings show that stock efficiency evaluation under the new framework is also effective. The efficiency values indicate that the portfolio frontier under the new framework is more externally enveloped than the DEA efficient surface under the standard DEA framework.展开更多
This paper introduces and represents conditional coherent risk measures as essential suprema of conditional expectations over a convex set of probability measures and as distorted expectations given a concave distorti...This paper introduces and represents conditional coherent risk measures as essential suprema of conditional expectations over a convex set of probability measures and as distorted expectations given a concave distortion function.A model is then developed for the bid and ask prices of a European-type asset by a conic formulation.The price process is governed by a modified geometric Brownian motion whose drift and diffusion coefficients depend on a Markov chain.The bid and ask prices of a European-type asset are then characterized using conic quantization.展开更多
In this paper,we first construct a time consistent multi-period worst-case risk measure,which measures the dynamic investment risk period-wise from a distributionally robust perspective.Under the usually adopted uncer...In this paper,we first construct a time consistent multi-period worst-case risk measure,which measures the dynamic investment risk period-wise from a distributionally robust perspective.Under the usually adopted uncertainty set,we derive the explicit optimal investment strategy for the multi-period robust portfolio selection problem under the multi-period worst-case risk measure.Empirical results demonstrate that the portfolio selection model under the proposed risk measure is a good complement to existing multi-period robust portfolio selection models using the adjustable robust approach.展开更多
When executing a large order of stocks in a market,one important factor in forming the optimal trading strategy is to consider the price impact of large-volume trading activity.Minimizing a risk measure of the impleme...When executing a large order of stocks in a market,one important factor in forming the optimal trading strategy is to consider the price impact of large-volume trading activity.Minimizing a risk measure of the implementation shortfall,i.e.,the difference between the value of a trader’s initial equity position and the sum of cash flow he receives from his trading process,is essentially a stochastic control problem.In this study,we investigate such a practical problem under a dynamic coherent risk measure in a market in which the stock price dynamics has a feature of momentum effect.We develop a fast approximation solution scheme,which is critical in highfrequency trading.We demonstrate some prominent features of our derived solution algorithm in providing useful guidance for real implementation.展开更多
In this work we give a comprehensive overview of the time consistency property of dynamic risk and performance measures,focusing on a the discrete time setup.The two key operational concepts used throughout are the no...In this work we give a comprehensive overview of the time consistency property of dynamic risk and performance measures,focusing on a the discrete time setup.The two key operational concepts used throughout are the notion of the LMmeasure and the notion of the update rule that,we believe,are the key tools for studying time consistency in a unified framework.展开更多
For the multiplicative background risk model,a distortion-type risk measure is used to measure the tail risk of the portfolio under a scenario probability measure with multivariate regular variation.In this paper,we i...For the multiplicative background risk model,a distortion-type risk measure is used to measure the tail risk of the portfolio under a scenario probability measure with multivariate regular variation.In this paper,we investigate the tail asymptotics of the portfolio loss ∑_(i=1)^(d)R_(i)S,where the stand-alone risk vector R=(R_(1),...,R_(d))follows a multivariate regular variation and is independent of the background risk factor S.An explicit asymptotic formula is established for the tail distortion risk measure,and an example is given to illustrate our obtained results.展开更多
基金Supported by the National Social Science Foundation of China(21CTJ005)the Anhui Provincial Natural Science Foundation(KJ2017A105)。
文摘Affected by the Federal Reserve's interest rate hike and the downward pressure on the domestic economy,the phenomenon of default is still prominent.The credit risk of the listed companies has become a growing concern of the community.In this paper we present a novel credit risk measurement method based on a dimensional reduation technique.The method first extracts the risk measure indexes from the basal financial data via dimensional reduation by using deep belief network(DBN),exploratory factor analysis(EFA)and confirmatory factor analysis(CFA)in turn.And then the credit risk is measured by a systemic structural equation model(SEM)and logistic distribution.To validate the proposed method,we employ the financial data of the listed companies from Q12019 to Q22022.The empirical results show its effectiveness on statistical evaluation,assessment on testing samples and credit risk forecasting.
基金supported by the National Natural Science Foundation of China (11901184, 11771343)the Natural Science Foundation of Hunan Province (2020JJ5025)。
文摘In this paper, we focus on anticipated backward stochastic Volterra integral equations(ABSVIEs) with jumps. We solve the problem of the well-posedness of so-called M-solutions to this class of equation, and analytically derive a comparison theorem for them and for the continuous equilibrium consumption process. These continuous equilibrium consumption processes can be described by the solutions to this class of ABSVIE with jumps.Motivated by this, a class of dynamic risk measures induced by ABSVIEs with jumps are discussed.
文摘Deep foundation pit excavation is a basic and key step involved in modern building construction.In order to ensure the construction quality and safety of deep foundation pits,this paper takes a project as an example to analyze deep foundation pit excavation technology,including the nature of this construction project,the main technical measures in the construction of deep foundation pit,and the analysis of the safety risk prevention and control measures.The purpose of this analysis is to provide scientific reference for the construction quality and safety of deep foundation pits.
文摘This study explored the effects of ambiguity on the calculation of Value-at-Risk(VaR)using a mathematical model based on the theory of Choquet-Brownian processes.It was found that while a moderate degree of ambiguity aversion yields a higher value for VaR and Expected Shortfall(ES),the result can be reversed in a deeply ambiguous environment.Additionally,some sufficient conditions are provided for the preservation of this effect under various forms of risk aggregation.This study offers a new perspective to full awareness on capital requirement calculation as requested by international regulation.
基金This study was funded by the MITACS Accelerate Grant-Award Number IT12339the Foreign Young Talents Program of the Ministry of Science and Technology of China(QN20200017001)the China Postdoctoral Science Foundation(2020M672913).
文摘This study considers the risk management of insurance policies in line with the implementation of the new International Financial Reporting Standards 17.It applies the paid-incurred chain method to model the future unpaid losses by combining the information channels of both the incurred claims and paid losses.We propose the recovery of the empirical distribution of the outstanding claims liabilities associated with a group of contracts via moment-based density approximation.We determine the risk measures and adjustments that are compliant with the new standard using the Monte–Carlo simulation method and approximated distributions.The historical data on the aggregate Ontario automobile insurance claims over a 15-year period are analyzed to examine the appropriateness and accuracy of our approach.
文摘This paper presents explicit formulae giving tight upper and lower bounds on the expectations of alpha-unimodal random variables having a known range and given set of moments. Such bounds can be useful in ordering of random variables in terms of risk and in PERT analysis where there is only incomplete stochastic information concerning the variables under investigation. Explicit closed form solutions are also given involving alpha-unimodal random variables having a known mean for two particularly important measures of risk—the squared distance or variance, and the absolute deviation. In addition, optimal tight bounds are given for the probability of ruin in the collective risk model when the severity distribution has an alpha-unimodal distribution with known moments.
文摘Reinsurance is an effective risk management tool for insurers to stabilize their profitability. In a typical reinsurance treaty, an insurer cedes part of the loss to a reinsurer. As the insurer faces an increasing number of total losses in the insurance market, the insurer might expect the reinsurer to bear an increasing proportion of the total loss, that is the insurer might expect the reinsurer to pay an increasing proportion of the total claim amount when he faces an increasing number of total claims in the insurance market. Motivated by this, we study the optimal reinsurance problem under the Vajda condition. To prevent moral hazard and reflect the spirit of reinsurance, we assume that the retained loss function is increasing and the ceded loss function satisfies the Vajda condition. We derive the explicit expression of the optimal reinsurance under the TVaR risk measure and TVaR premium principle from the perspective of both an insurer and a reinsurer. Our results show that the explicit expression of the optimal reinsurance is in the form of two or three interconnected line segments. Under an additional mild constraint, we get the optimal parameters and find the optimal reinsurance strategy is full reinsurance, no reinsurance, stop loss reinsurance, or quota-share reinsurance. Finally, we gave an example to analyze the impact of the weighting factor on optimal reinsurance.
文摘Tail risk is a classic topic in stressed portfolio optimization to treat unprecedented risks,while the traditional mean–variance approach may fail to perform well.This study proposes an innovative semiparametric method consisting of two modeling components:the nonparametric estimation and copula method for each marginal distribution of the portfolio and their joint distribution,respectively.We then focus on the optimal weights of the stressed portfolio and its optimal scale beyond the Gaussian restriction.Empirical studies include statistical estimation for the semiparametric method,risk measure minimization for optimal weights,and value measure maximization for the optimal scale to enlarge the investment.From the outputs of short-term and long-term data analysis,optimal stressed portfolios demonstrate the advantages of model flexibility to account for tail risk over the traditional mean–variance method.
基金supported by the National Social Science Fund of China under Grant No.22BTJ027。
文摘The paper presents the properties of an alternative method,which measures market risk over time-horizon exceeding one day:Mark to market value at risk(MMVaR).Relying on the minimal returns during the time interval,this method not only considers the non-normality of data and information about sample size,but also meets the requirement of increasing the minimal capital ratio in BaselⅢ,basically.The authors theoretically prove the translation invariance,monotonicity and subadditivity of MMVaR as a risk measure under some conditions,and study its finite sample properties through Monte Carlo simulations.The empirical analysis shows that MMVaR can measure multi-period risk accurately.
文摘We study mean-field BSDEs with jumps and a generalized mean-field operator that can capture higher-order interactions.We interpret the BSDE solution as a dynamic risk measure for a representative bank whose risk attitude is influenced by the system.This influence can come in a wide class of choices,including the average system state or average intensity of system interactions.Using Fenchel−Legendre transforms,our main result is a dual representation for the expectation of the risk measure in the convex case.In particular,we exhibit its dependence on the mean-field operator.
基金supported by Natural Science Foundation of China and Jiangsu Province(No.11871050,No.11971342,No.11401414,No.BK20140299,No.14KJB110022)。
文摘G-VaR,which is a type of worst-case value-at-risk(VaR),is defined as measuring risk incorporating model uncertainty.Compared with most extant notions of worst-case VaR,G-VaR can be computed using an explicit formula,and can be applied to large portfolios of several hundred dimensions with low computational cost.We also apply G-VaR to robust portfolio optimization,thereby providing a tractable means to facilitate optimal allocations under the condition of market ambiguity.
基金supported by the Important Natural Science Foundation of Colleges and Universities of Anhui Province under Grant No.KJ2020A0122the Scientific Research Start-up Foundation of Hefei Normal University。
文摘In the context of multivariate regular variation,the authors establish the first-order asymptotics of the spectral risk measure of portfolio loss.Furthermore,by the notion of second-order regular variation,the second-order asymptotics of the spectral risk measure of portfolio loss is also presented.In order to illustrate the derived results,a numerical example with Monte Carlo simulation is carried out.
基金the support from the Natural Sciences and Engineering Research Council of Canada(NSERC)(grant No.RGPIN-2016-03975)supported by grants from the National Natural Science Foundation of China(Grant No.11971505)111 Project of China(No.B17050).
文摘Reinsurance is an effective way for an insurance company to control its risk.How to design an optimal reinsurance contract is not only a key topic in actuarial science,but also an interesting research question in mathematics and statistics.Optimal reinsurance design problems can be proposed from different perspectives.Risk measures as tools of quantitative risk management have been extensively used in insurance and finance.Optimal reinsurance designs based on risk measures have been widely studied in the literature of insurance and become an active research topic.Different research approaches have been developed and many interesting results have been obtained in this area.These approaches and results have potential applications in future research.In this article,we review the recent advances in optimal reinsurance designs based on risk measures in static models and discuss some interesting problems on this topic for future research.
基金supported by the Swedish Civil Contingencies Agency(MSB)the Swedish Government through the Centre for Natural Disaster Science(CNDS)the Faculty of Health,Science and Technology at Karlstad University
文摘Natural events such as floods and landslides can have severe consequences.The risks are expected to increase,both as a consequence of climate change and due to increased vulnerabilities,especially in urban areas.Although preventive measures are often cost-effective,some measures are beneficial to certain values,while some may have negative impacts on other values.The aim of the study presented here was to investigate two frameworks used for assessing the effectiveness and sustainability of physical and nonphysical flood and landslide risk reduction measures.The study is based on literature,available information from authorities and municipalities,expert knowledge and experience,and stakeholder views and values.The results indicate that the risks for suboptimization or maladaptation are reduced if many aspects are included and a broad spectrum of stakeholders are involved.The sustamability assessment tools applied here can contribute to a more transparent and sustainable risk management process by assessing strategies and interventions with respect to both short- and long-term perspectives,including local impacts and wider environmental impacts caused by climate change,for example.The tools can also cover social and economic aspects.The assessment tools provide checklists that can support decision processes,thus allowing for more transparent decisions.
基金supported by the National Natural Science Foundation of China under Grant Nos.72071192,71671172the Anhui Provincial Quality Engineering Teaching and Research Project Under Grant No.2020jyxm2279+2 种基金the Anhui University and Enterprise Cooperation Practice Education Base Project under Grant No.2019sjjd02Teaching and Research Project of USTC(2019xjyxm019,2020ycjg08)the Fundamental Research Funds for the Central Universities(WK2040000027)。
文摘This paper proposes a new approach for stock efficiency evaluation based on multiple risk measures. A derived programming model with quadratic constraints is developed based on the envelopment form of data envelopment analysis(DEA). The derived model serves as an input-oriented DEA model by minimizing inputs such as multiple risk measures. In addition, the Russell input measure is introduced and the corresponding efficiency results are evaluated. The findings show that stock efficiency evaluation under the new framework is also effective. The efficiency values indicate that the portfolio frontier under the new framework is more externally enveloped than the DEA efficient surface under the standard DEA framework.
文摘This paper introduces and represents conditional coherent risk measures as essential suprema of conditional expectations over a convex set of probability measures and as distorted expectations given a concave distortion function.A model is then developed for the bid and ask prices of a European-type asset by a conic formulation.The price process is governed by a modified geometric Brownian motion whose drift and diffusion coefficients depend on a Markov chain.The bid and ask prices of a European-type asset are then characterized using conic quantization.
基金This research was supported by the National Natural Science Foundation of China(Nos.71371152 and 11571270).
文摘In this paper,we first construct a time consistent multi-period worst-case risk measure,which measures the dynamic investment risk period-wise from a distributionally robust perspective.Under the usually adopted uncertainty set,we derive the explicit optimal investment strategy for the multi-period robust portfolio selection problem under the multi-period worst-case risk measure.Empirical results demonstrate that the portfolio selection model under the proposed risk measure is a good complement to existing multi-period robust portfolio selection models using the adjustable robust approach.
文摘When executing a large order of stocks in a market,one important factor in forming the optimal trading strategy is to consider the price impact of large-volume trading activity.Minimizing a risk measure of the implementation shortfall,i.e.,the difference between the value of a trader’s initial equity position and the sum of cash flow he receives from his trading process,is essentially a stochastic control problem.In this study,we investigate such a practical problem under a dynamic coherent risk measure in a market in which the stock price dynamics has a feature of momentum effect.We develop a fast approximation solution scheme,which is critical in highfrequency trading.We demonstrate some prominent features of our derived solution algorithm in providing useful guidance for real implementation.
基金Tomasz R.Bielecki and Igor Cialenco acknowledge support from the NSF grant DMS-1211256.Part of the research was performed while Igor Cialenco was visiting the Institute for Pure and Applied Mathematics(IPAM),which is supported by the National Science Foundation.Marcin Pitera acknowledges the support by Project operated within the Foundation for Polish Science IPP Programme“Geometry and Topology in Physical Model”co-financed by the EU European Regional Development Fund,Operational Program Innovative Economy 2007–2013.
文摘In this work we give a comprehensive overview of the time consistency property of dynamic risk and performance measures,focusing on a the discrete time setup.The two key operational concepts used throughout are the notion of the LMmeasure and the notion of the update rule that,we believe,are the key tools for studying time consistency in a unified framework.
基金supported by the National Key Research and Development Plan(No.2016YFC0800100)the NSFC of China(Nos.11671374,71771203,71631006).
文摘For the multiplicative background risk model,a distortion-type risk measure is used to measure the tail risk of the portfolio under a scenario probability measure with multivariate regular variation.In this paper,we investigate the tail asymptotics of the portfolio loss ∑_(i=1)^(d)R_(i)S,where the stand-alone risk vector R=(R_(1),...,R_(d))follows a multivariate regular variation and is independent of the background risk factor S.An explicit asymptotic formula is established for the tail distortion risk measure,and an example is given to illustrate our obtained results.
