Optimal Strategies for an Ambiguity-Averse Insurer under a Jump-Diffusion Model and Defaultable Risk

Abstract

In this paper, we consider a robust optimal investment-reinsurance problem with a default risk. The ambiguity-averse insurer (AAI) may carry out transactions on a risk-free asset, a stock, and a defaultable corporate bond. The stock’s price is described by a jump-diffusion process, and both the jump intensity and the distribution of jump amplitude are uncertain, i.e., the jump is ambiguous. The AAI’s surplus process is assumed to follow an approximate diffusion process. In particular, the reinsurance premium is calculated according to the generalized mean-variance premium principle, and the reinsurance type has to follow a self-reinsurance function. In performing dynamic programming, both the predefault case and the postdefault case are analyzed, and the optimal strategies and the corresponding value functions are derived under the worst-case scenario. Moreover, we give a detailed proof of the verification theorem and give some special cases and numerical examples to illustrate our theoretical results.