This paper considers an optimal reinsurance-investment problem foran insurer, who aims to minimize the risk measured byCapital-at-Risk (CaR) with the constraint that the expected terminalwealth is not less than a predefined level. The surplus of theinsurer is described by a Brownian motion with drift. The insurercan control her/his risk by purchasing proportional reinsurance,acquiring new business, and investing her/his surplus in a financialmarket consisting of one risk-free asset and multiple risky assets.Three mean-CaR models are constructed. By transforming these modelsinto bilevel optimization problems, we derive the explicitexpressions of the optimal deterministic rebalancereinsurance-investment strategies and the mean-CaR efficientfrontiers. Sensitivity analysis of the results and a numericalexample are provided.
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Zeng et al. (2012) studied this question.