The Utility Indifference Pricing Under Rough Heston Model

Based on mathematical tools such as stochastic analysis and stochastic control theory,this thesis studies the utility indifference pricing problem based on the rough Heston model in incomplete financial markets.Due to the existence of multiple equivalent martingale measures in an incomplete market,it is impossible to create a fully replicated portfolio,and traditional option pricing methods such as B-M-S cannot be used.Therefore,this thesis studies the utility indifference pricing.This thesis assumes that the financial market consists of a risk-free asset,a stock that obeys the rough Heston model,and a non-tradable asset that obeys geometric Brownian motion.In view of the two situations where investors do not purchase and purchase options with non-tradable assets as the underlying at the initial moment,the optimal investment portfolio problem is constructed respectively.Using the equality of the utility maximizationIn of these two cases,the utility indifference price is achieved.Compared to the classic Heston model,the rough Heston model can better reflect the microstructure of the market.So that it is more in line with the current actual financial market.However,this model does not have markov and semi-martingale properties,so it cannot directly use the classic dynamic programming principles to solve the optimal portfolio.This thesis approximates the rough Heston model with a finite-dimensional multi-factor stochastic volatility model,and then approximates the optimal portfolio problem and the indifference pricing problem under the rough Heston model,and applies the dynamic programming principle under the power utility function to derive the HJB equation.Explicit solutions to the optimal strategy and value function are achieved.Finally,numerical experiments are used to analyze the influence of model roughness,the correlation coefficient of the stock price process and the volatility process,volatility parameter and the investor's risk aversion coefficient on investment strategy and value function.And the economic explanation is given.