本文選題：指數效用無差異效用價值過程 + 一般跳過程　； 參考：《中國科學:數學》2015年10期

【摘要】：本文采用指數效用最大化的方法研究了期權的動態(tài)無差異效用價值過程Ct(H;α).考慮股票價格過程為具有基于隨機測度的一般跳的半鞅模型,且期權的無差異效用價值過程的Doob-Meyer分解的鞅部分的GKW(Galtchouk-Kunita-Watanabe)分解滿足Jacod鞅表示定理.利用無差異效用價值過程在最小熵測度和最優(yōu)投資策略下為鞅的事實構建了一個倒向隨機微分方程.通過概率測度變換將方程的鞅部分和生成元轉化為BMO(bounded mean oscillation)鞅,證明了該方程的解的唯一性.并將方程的生成元分成[?A=0]和[?A≠0],證明了最優(yōu)投資策略存在.從而給出期權無差異效用價值過程的倒向隨機微分方程的表達形式.
[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，

本文編號：1930309