Economic Rationale for Reinsurance Stochastic Models

The following is a brief outline of some stochastic actuarial and financial models that can be used for a quantitative analysis of the economic rationale for reinsurance. Such a careful quantification of the microeconomics of reinsurance and the tangible value created for the client lies at the very heart of Swiss Re’s value proposition for reinsurance. This technical note is written for practitioners with a mathematical background. We have tried to keep the mathematics as simple and straightforward as possible. Furthermore, for the reader’s convenience, we have listed a number of reference texts for further study at the end of this note. Also, all the models are available in software form (using Microsoft EXCEL as a user interface).

We start our quantitative analysis of the economic rationale for reinsurance by considering one line of business. Here, line of business means some homogeneous block of insurance or reinsurance business, for example UK Life, US Medex, P&C Asia Pacific, etc., depending on the level of detail at which the economic rationale and the value proposition for reinsurance are to be quantified. In a first step, we develop a dynamic stochastic model that describes the evolution of claims, premiums, reserves and expenses for this line of business over time. We then focus our attention on the estimation of claims severity, the estimation of claims frequency, the variation of risk propensity due to trends (e.g., improvements in mortality rates in life insurance, worsening claims experience in some areas of health insurance, etc.) and cycles (e.g., flu epidemics, etc.), and finally, on the effect of the three major reinsurance arrangements: quota share reinsurance, surplus reinsurance and stop loss reinsurance.

On the company level, we first develop a dynamic stochastic model for the solvency margin or risk reserve which allows us to determine the capital at risk as a function of the reinsurance arrangements in force and the client’s strategic allocation of assets. Note that we do not treat assets and liabilities separately here; for both the same simple and consistent methodological framework is used. This is very much in line with today’s state-of-the-art asset/liability management strategies. Furthermore, the model can be applied to quantify the effects of reinsurance (and, more generally, of asset/liability management strategies) on a cedent, an insurer and a reinsurer simultaneously. Having determined capital at risk, we show how to implement a consistent system of performance measurement ("efficient frontier" approach) for insurance and reinsurance companies and that reinsurance creates tangible value by moving the insurer’s efficient frontier in the direction of higher returns and lower risk. As a final point in this section of the technical note, we show how the same methodology can be used to (a) develop a consistent system of performance measurement for internal operational units of the insurer and the reinsurer and (b) develop a consistent, best practice pricing approach for insurance and reinsurance contracts.

In a final section of this document, we look at how the mathematical models used to quantify the economic rationale for reinsurance can also be used to implement new value proposition (VP) based client solutions and can therefore provide the reinsurer with new market and profit growth opportunities.