Using Cat Models for Optimal Risk Allocation of P&C Liability Portfolios

This article provides a general introduction to using catastrophe models to optimally manage the risk of a portfolio of Property & Casualty (P&C) liabilities. There is increasing emphasis on the enterprise‐wide allocation of risk capacity for all financial intermediaries, e.g. banks, pensions, investment funds, as well as life and P&C insurers. The optionality (the skewness, kurtosis, and correlation with asset risk) of liability risks contribute substantially to earnings volatility. The severity of low‐probability events, i.e. natural catastrophes (e.g. hurricanes, earthquakes), combined with increases in geographic concentrations of wealth can adversely affect the diversification of the liability risk at the portfolio level. Since in both finance and insurance, optimally allocating risk at the portfolio level is generally based on (linear) combinations of nonlinear risks, finding an optimal allocation is not always tractable. The author describes a well‐established optimization algorithm and produces a reasonable approximation for an optimal solution.