Optimal proportional reinsurance-investment policies for an insurer under Capital-at-Risk constraint
风险资本约束下保险公司的最优比例再保险–投资策略

This paper investigates a reinsurance-investment problem for an insurer. Assume that the integral risk of the insurer is measured by Capital-at-Risk(CaR), the surplus process is described by a diffusion approximation model; the insurer is allowed to purchase proportional reinsurance(or acquire new business) and to invest on a risk-free asset and multiple risky assets at any time; the prices of risky assets are driven by the model of geometric Brownian motions. The target of the insurer is to maximize the expectation of the terminal wealth under a CaR constraint. Two mean-CaR models are established for the problem. Explicit expressions of the optimal policies and ef cient frontiers to the models are derived by using a hierarchical optimization method and the variational calculus approach.