Dynamic mean‐variance and optimal reinsurance problems under the no‐bankruptcy constraint for an insurer

In this paper, we consider the optimal investment and optimal reinsurance problems for an insurer under the criterion of mean‐variance with bankruptcy prohibition, i.e., the wealth process of the insurer is not allowed to be below zero at any time. The risk process is a diffusion model and the insurer can invest in a risk‐free asset and multiple risky assets. In view of the standard martingale approach in tackling continuous‐time portfolio choice models, we consider two subproblems. After solving the two subproblems respectively, we can obtain the solution to the mean‐variance optimal problem. We also consider the optimal problem when bankruptcy is allowed. In this situation, we obtain the efficient strategy and efficient frontier using the stochastic linear‐quadratic control theory. Then we compare the results in the two cases and give a numerical example to illustrate our results.