Abstract: The objective of this paper is to investigate optimal investment strategy for a pharmaceutical or petroleum company under mean-variance criterion. The surplus of the company is modeled as a dual risk model. We assume that the company can invest into a risk-free asset and n risky assets. Short-selling and borrowing money are allowed. Since this problem is time-inconsistent, we study it within a game theoretical framework. The subgame perfect Nash equilibrium strategies (namely time-consistent strategies) are derived by solving the Extended Hamilton-Jacobi-Bellman(HJB) equations in the classic diffusion dual model and in the diffusion dual approximation model, separately. Surprisingly when a coefficient parameter ρ = 0, optimal time-consistent investment strategies and the value functions have the same expressions in both cases. Finally, We present economics implications and provide sensitivity analysis for our results by numerical examples.

Keywords: Optimal time-consistent investment, Extended Hamilton-Jacobi-Bellman equation, Mean-variance criterion

Pages: 213-225