随机波动率模型的最小熵鞅测度和效用无差别定价

Minimal Entropy Martingale Measure and Utility Indifference Pricing in the Stochastic Volatility Model

本文研究了随机波动率模型的最小熵鞅测度和效用无差别定价。利用动态规划方法,得到了效用无差别定价满足的偏微分方程以及效用无差别套期保值策略。利用指数效用函数的最优投资策略与最小熵鞅测度之间的关系,证明了最小熵鞅测度的存在性,并利用偏微分方程给出了最小熵鞅测度。

This paper deals with the minimal pricing concerning a stochastic volatility model. entropy martingale measure and utility indifference The classical dynamic programming approach leads to the partial differential equation that satisfies utility indifference pricing, and obtains the indifference hedging strategy. Using the relationship between the minimal entropy martingale measure and the optimal investment strategy with an exponential utility, the existence of the minimal entropy martingale measure is proved, and can be expressed in terms of the solution to the PDE.