The CEV-SV Model - Portfolio Optimization With CARA Utility Under Two Different Cases Of Prices Of Risk

Yang Xiaoye, Xiao Hongmin

CEV-SV model, expected utility theory, two different cases of prices of risk.

In this paper,we consider a new diffusion models for stock prices with applications in portfolio optimization to overcome the main restriction of the CEV model. The diffusion model combines constant elasticity of volatility(CEV) and stochastic volatility (SV) to create the CEV-SV model,while the SV component features the state-of-the-art 4/2 model.So that the complete correlation between the price of risky asset and its volatility is decoupled, and added randomness between the price of risky assets and their volatility.It can be clearly noticed that when ,the CEV-SV Model degenerates to SV Model.We study an investment problem within expected utility theory (EUT) for incomplete markets, producing closed-form representations for the optimal strategy for two different cases of prices of risk on the stock.Finally,numerical examples are provided to support our theoretical results.We find that under the first risk price, the optimal investment strategy exhibits reduced stability and is more susceptible to stock price volatility.Therefore, it is advisable for different investors to adopt distinct investment strategies. Specifically, risk-averse or neutral investors may find it suitable to invest under the second risk price, while risk-loving investors may prefer investing under the first risk price.And the numerical simulation also tells us that the presence of CEV component incites a sharp downward movements in the optimal allocation toward short maturities.