Optimizing a Multi-Season Catastrophe Reinsurance Program With Private and Public Components

As risk-bearing organizations and the public at large have recognized the long-term frequency and potential magnitude of natural disasters, risk management solutions have emerged from both private enterprise and the public sector. A primary property insurer should choose a combination of ceded reinsurance, internal capital, and capital market products which minimizes its expected total cost of insuring consumers against catastrophes over a multi-year horizon, subject to risk tolerance and operating constraints. For this problem, the traditional metric of gross single event "probable maximum loss" is inadequate; a standard considering "'probable aggregate retained loss" over the decision horizon is better. The development of Dynamic Financial Analysis (DFA) to date has not given sufficient attention to natural disasters, the greatest threat to the solvency of many carriers. This paper shows how a property insurer can use commercial catastrophe models, public databases, some DFA concepts, and desktop computing tools to overcome two obstacles to integrating internal, private market, and public sector capital sources into an optimal program: Uncertainty about the market-wide impact of event frequency and severity over several seasons, which determines the response of the public reinsurer to the individual insurer. • The complexity of the interactions between the responses of private and public programs to event experience. The concepts and methods presented in this example may be generalized to solve a host of reinsurance program design problems involving multiple disjoint risk transfer vehicles. The implications for the optimal strategy of the insurer of the decisions of public policy makers and the insurer's level of commitment to the market will be a backdrop to the analysis. Integration of the results into enterprise-wide DFA will be considered.