基于超前倒向随机微分方程的动态风险度量

DYNAMIC RISK MEASUREMENT VIA ANTICIPATED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

本文研究了基于超前倒向随机微分方程的时间相容的过程的动态凸(一致性)风险度量的问题.利用对超前倒向随机微分方程生成元的适当假设,建立超前倒向随机微分方程生成元与过程的动态凸(一致性)风险度量的对应模型,证明了超前倒向随机微分方程的解可以定义时间相容的过程的风险度量.得到了基于超前倒向随机微分方程的风险度量,推广了基于倒向随机微分方程的动态风险度量.由于超前倒向随机微分方程生成元中包含当前时刻和未来时刻的解,因此本文的结论对风险的预测更加可靠.

This paper studies the problem of time-consistent dynamic convex(coherent) risk measures for processes via anticipated backward stochastic differential equations. Using appropriate assumptions on the generator of the anticipated backward stochastic differential equation,the corresponding model of the anticipated backward stochastic differential equation generator and the dynamic convex(coherent) risk measure of the process is established, which proves that the solution of the anticipated backward stochastic differential equation can be defined for the risk measurement of time-consistent processes, the risk measurement based on the anticipated backward stochastic differential equation is obtained, and the dynamic risk measurement based on the backward stochastic differential equation is extended. Because the anticipated backward stochastic differential equations generator contains the current and future solutions, the conclusion of this paper is more reliable for risk prediction.