An insurer's optimal strategy towards a new independent business

In this paper, we investigate the optimal decision making of an insurer towards a new insurable business, whose risk is independent of the existing risk faced by the insurer. We assume that the insurer, with the objective of maximizing the expected utility of its final wealth, together with the solvency constraint and the availability of reinsurance as a risk transfer mechanism, is deciding if it is viable to underwrite a new insurance business risk. If this new business is underwritten, it is shown that a stop-loss reinsurance contract is optimal when the solvency risk is quantified by the conditional value at risk. If the regulatory regime changes to the value at risk, the optimal reinsurance form becomes more complicated; it can be either stop-loss or two-layer under the assumption that the new risk has a strictly decreasing probability density function. Numerical examples are provided to illuminate the insurer's decision making and the optimal form of the reinsurance strategy.