Optimal reinsurance with a systemic surplus shock

Abstract

We examine the optimal reinsurance and asset allocation strategies for an insurer who minimizes the ruin probability and faces a systemic surplus shock. Analytically tractable solutions are obtained when this shock occurs at an uncertain time. We then demonstrate that the systemic surplus shock results in a nonstandard form of market incompleteness, which alters both qualitative and quantitative features of existing strategies without the surplus shock. In particular, a specific form of the marginal value for the insurer’s minimized ruin probability plays a key role in the characterization of optimal policies with the systemic surplus shock.