微分对策方法在期权定价中的应用:理论分析

A Differential Game Approach to Option Pricing: Theoretical Analysis

在最差情况最优的框架下研究存在交易费用时的期权定价问题．在风险厌恶的假设条件下，运用微分对策的上值、下值和值分别给出了期权买价、卖价和公平价格的定义．通过微分对策的降维把期权定价问题归结为求解微分对策的值函数．基于微分对策理论推导出了该值函数满足的偏微分方程．

Option pricing in the presence of transaction costs is investigated in the framework of worst-case optimization. Under the assumption of risk-aversion, option writing price, buying price and fair price are defined respectively with the upper value, the lower value and the value of a differen- tial game. Through the reduction of the differential game in dimension, the pricing problem is trans- formed into solving the value function of another differential game. A partial differential equation is obtained for the value function by using the theory of differential games.