Research on the Optimal Investment Strategy with Jumps When Risks Cannot Be Hedged

The problem of the optimal investment strategy has always been a key research content in modern finance. Since stock prices in real financial markets often experience jumps, and the randomness of investors' labor income contributes to risks that cannot be completely hedged, it is necessary to consider these factors in investment strategy design. This paper studies the continuous-time dynamic mean-variance portfolio selection problem when the risk is not hedged. It is assumed that the price of risky assets follows a jump-diffusion process. The investor's goal is to minimize the variance of the wealth at the terminal time under the condition of a given expected terminal wealth. By solving the corresponding Hamilton-Jacobi-Bellman equation of the model, the viscosity solution of the optimal investment strategy is obtained. The results show that the jump factors in the price process and the unhedged risk have an impact on the optimal investment strategy that cannot be ignored.