具有一般跳过程的期权无差异效用价值过程的定价模型

发布时间：2018-05-24 19:43

  本文选题：指数效用无差异效用价值过程 + 一般跳过程　； 参考：《中国科学:数学》2015年10期

【摘要】：本文采用指数效用最大化的方法研究了期权的动态无差异效用价值过程Ct(H;α).考虑股票价格过程为具有基于随机测度的一般跳的半鞅模型,且期权的无差异效用价值过程的Doob-Meyer分解的鞅部分的GKW(Galtchouk-Kunita-Watanabe)分解满足Jacod鞅表示定理.利用无差异效用价值过程在最小熵测度和最优投资策略下为鞅的事实构建了一个倒向随机微分方程.通过概率测度变换将方程的鞅部分和生成元转化为BMO(bounded mean oscillation)鞅,证明了该方程的解的唯一性.并将方程的生成元分成[?A=0]和[?A≠0],证明了最优投资策略存在.从而给出期权无差异效用价值过程的倒向随机微分方程的表达形式.
[Abstract]:In this paper, the exponential utility maximization method is used to study the dynamic nondifferential-utility value process of options. Considering that the stock price process is a semimartingale model with a general jump based on random measure, and the Doob-Meyer decomposition of the nondifferential-utility value process of an option satisfies the Jacod martingale representation theorem, the GKW Galtchouk-Kunita-Watanabe decomposition satisfies the Jacod martingale representation theorem. In this paper, a backward stochastic differential equation is constructed by using the fact that the non-differential utility value process is a martingale under the minimum entropy measure and the optimal investment strategy. The martingale partial sum of the equation is transformed into BMO(bounded mean oscillation martingale by the transformation of probability measure, and the uniqueness of the solution of the equation is proved. The generator of the equation is divided into two parts: [A0] and [A 鈮，

本文编号：1930309