Optimal reinsurance under general law-invariant convex risk measure and TVaR premium principle

Abstract

In this paper, we study the optimal reinsurance problem where risks of the insurer are measured by general law-invariant risk measures and premiums are calculated under the TVaR premium principle, which extends the work of the expected premium principle. Our objective is to characterize the optimal reinsurance strategy which minimizes the insurer’s risk measure of its total loss. Our calculations show that the optimal reinsurance strategy is of the multi-layer form, i.e., f∗ (x) = x ∧ c∗ + (x − d∗)+ with c∗ and d∗ being constants such that 0 ≤ c∗ ≤ d∗.