Modeling financial reinsurance in the casualty insurance business via stochastic programming

In this paper we examine the rationale for financial reinsurance in the casualty insurance business. As opposed to regular reinsurance, financial reinsurance refers to an investment strategy that uses the financial markets to hedge insurance risk. The casualty insurer takes positions in derivatives on underlying assets whose prices are highly positively or negatively correlated with specific insurance risks. We formulate the asset liability management problem for a mutually owned casualty insurer, in the context of a dynamic stochastic portfolio selection model. Using numerical studies of the resulting large-scale nonlinear program, we compare properties of optimal portfolios with and without the possibility of financial reinsurance. We let an alleged representative policyholder, endowed with a linear plus negative exponential utility function, evaluate the various optimal portfolios. When policyholders' utility functions exhibit reasonable levels of risk aversion, we find that portfolios reflecting financial reinsurance dominate portfolios that are not financially reinsured.