论文部分内容阅读
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.
In this paper, we use the exponential utility maximization method to study the dynamic undifferentiated utility value process Ct (H; α) of the options. Considering the stock price process as a semi-martingale model with general jump based on stochastic measure and the option’s no-difference utility value process The GKW (Galtchouk-Kunita-Watanabe) decomposition of the Doob-Meyer decomposition of the Doob-Meyer decomposition satisfies the Jacod martingale representation theorem. By using the differenceless utility value process, a backward randomization is constructed according to the fact that the minimum entropy measure and the optimal investment strategy are martingales The differential equation is obtained by transforming the martingale part and the generator of the equation into BMO (bounded mean oscillation) martingale by means of the probability measure transformation, which proves the uniqueness of the solution. The generator of the equation is divided into [? A = 0] and [ ? A ≠ 0], which proves that the optimal investment strategy exists, so as to give the expression of backward stochastic differential equation with no difference utility value process.