Optimal portfolio strategy of wealth process: a Lévy process model-based method

This paper is concerned with the optimal portfolio problem for a company that can invest in two risky assets, where a novel Lévy-process-driven model is constructed to describe the dynamics of the wealth process by using a constant elasticity of variance model and a jump-diffusion process. A delicately designed value function is proposed under the mean–variance criterion to reflect the optimal portfolio for the stochastic volatility model. By using the verification theorem, the desired optimal portfolio strategy is proposed by the solution to certain Hamilton–Jacobi–Bellman equations. Furthermore, the corresponding expressions are achieved by using the stochastic analysis theory. Finally, a numerical simulation example is provided to verify the effectiveness of the proposed optimal portfolio strategy.