Mean-variance portfolio selection in a jump-diffusion financial market with common shock dependence

This paper considers the optimal investment problem in a financial market with one risk-free asset and one jump-diffusion risky asset. It is assumed that the insurance risk process is driven by a compound Poisson process and the two jump number processes are correlated by a common shock. A general mean-variance optimization problem is investigated, that is, besides the objective of terminal condition, the quadratic optimization functional includes also a running penalizing cost, which represents the deviations of the insurer's wealth from a desired profit-solvency goal. By solving the Hamilton-Jacobi-Bellman (HJB) equation, we derive the closed-form expressions for the value function, as well as the optimal strategy. Moreover, under suitable assumption on model parameters, our problem reduces to the classical mean-variance portfolio selection problem and the efficient frontier is obtained.