This paper presents a new conceptual framework for measuring insurance profitability. The idea is to model the sequence of results that would be obtained by writing the business under consideration year after year. Each year premium stays the same, but losses are randomly sampled from a fixed loss distribution. Central to the framework is a capital management structure. This governs the payment of profit-sharing dividends to shareholders and it also includes the selection of a floor and a ceiling that constrain the range of surplus for the company. The company pays shareholders any excess surplus above the ceiling. On the other hand, if surplus falls below the floor, the company is liquidated. If results are extremely bad, the company goes bankrupt. When there is a bankruptcy, the investors do not need to make up the shortfall. The sequence of random loss results leads to a sequence of flows, called equity flows, to and from the investors. The sequence of surplus values is a Markov chain. The duration of any sequence depends on the loss results and the capital management parameters. The profitability of any multi-year sequence is measured as the internal rate of return (IRR) on those equity flows. Many sequences are randomly simulated to produce a distribution of multi-year shareholder returns.
The paper uses this paradigm to provide a fresh perspective for assessing the potential benefit to shareholders from the purchase of reinsurance by the insurance company. Conventional single-year approaches are implicitly skeptical of reinsurance. It cedes money that could otherwise boost shareholder profit and it also reduces the value of the shareholder’s insolvency put option. The multi-year sequence perspective reveals conditions under which reinsurance can boost shareholder return and reduce volatility. The paper concludes with sensitivity analysis of several capital management and reinsurance parameters and qualitative discussion on how to optimize profitability from this long-term return perspective.
The paper uses this paradigm to provide a fresh perspective for assessing the potential benefit to shareholders from the purchase of reinsurance by the insurance company. Conventional single-year approaches are implicitly skeptical of reinsurance. It cedes money that could otherwise boost shareholder profit and it also reduces the value of the shareholder’s insolvency put option. The multi-year sequence perspective reveals conditions under which reinsurance can boost shareholder return and reduce volatility. The paper concludes with sensitivity analysis of several capital management and reinsurance parameters and qualitative discussion on how to optimize profitability from this long-term return perspective.
