本文讨论在金融中有重要应用价值的,由Lévy过程驱动的倒向双重随机微分方程: Y_t=ξ+∫_t^T f(s,Y_(s-),U_s,Z_s)ds+∫_t^T g(s,Y_(s-),U_s,Z_s)dB_s -∫_t^TU_sdW_s-sum for i=1 to ∞ Z_s^(i)dH_s^(i)在系数g满足Lipschitz条件,...本文讨论在金融中有重要应用价值的,由Lévy过程驱动的倒向双重随机微分方程: Y_t=ξ+∫_t^T f(s,Y_(s-),U_s,Z_s)ds+∫_t^T g(s,Y_(s-),U_s,Z_s)dB_s -∫_t^TU_sdW_s-sum for i=1 to ∞ Z_s^(i)dH_s^(i)在系数g满足Lipschitz条件,f满足推广的Bihari条件:|f(t,y_1,u_1,z_1)-f(t,y_2,u_2,z_2)|~2≤c(t)k(|y_1-y_2|~2)+K(|u_1-u_2|~2+||z_1-z_2||~2)时,利用推广It公式、Picard迭代法和区间延拓过程,证明了上述方程F_t适应解的存在唯一性,推广了其它文献以前的结论.展开更多
基金supported by the Natural Science Foundation of Anhui Province(1508085QA03)the Distinguished Young Scholars Foundation of Anhui Province(1608085J06)the National Natural Science Foundation of China(11501009,11371029)
基金Supported in part by NNSFC(10901003)the Research Project of Natural Science Foundation of Anhui Provincial University(KJZ010B345) the Grant for Youth of Anhui Normal University (2009XQN56)
文摘本文讨论在金融中有重要应用价值的,由Lévy过程驱动的倒向双重随机微分方程: Y_t=ξ+∫_t^T f(s,Y_(s-),U_s,Z_s)ds+∫_t^T g(s,Y_(s-),U_s,Z_s)dB_s -∫_t^TU_sdW_s-sum for i=1 to ∞ Z_s^(i)dH_s^(i)在系数g满足Lipschitz条件,f满足推广的Bihari条件:|f(t,y_1,u_1,z_1)-f(t,y_2,u_2,z_2)|~2≤c(t)k(|y_1-y_2|~2)+K(|u_1-u_2|~2+||z_1-z_2||~2)时,利用推广It公式、Picard迭代法和区间延拓过程,证明了上述方程F_t适应解的存在唯一性,推广了其它文献以前的结论.
