Portfolio Allocation In A Levy-Type Jump-Diffusion Model With Nonlife Insurance Risk

We propose a model that integrates investment, underwriting, and consumption/dividend policy decisions for a nonlife insurer by using a risk control variable related to the wealth-income ratio of the firm. This facilitates the efficient transfer of insurance risk to capital markets since it allows to select simultaneously investments and underwriting volume. The model is particularly valuable for business lines with significant exposure to extreme events and disaster risk, as it accounts for features usually depicted during negative economic shocks and catastrophic events, such as Levy-type jump-diffusion dynamics for the financial log-returns that are in turn correlated with insurance premiums and liabilities, as well as worst-case scenarios in which policyholders in the insurance portfolio report claims with the same severity simultaneously. Using the martingale method, we determine an optimal solvency threshold or wealth-income ratio, and investment strategy that maximizes the expected utility from dividend payouts that follows a (possibly stochastic) consumption clock. We illustrate the main results with numerical examples for log- and power-utility functions, and (bounded variation) tempered stable Levy jumps.