A Cost-of-Capital Risk Margin Formula for Nonlife Insurance Liabilities

By Glenn G. Meyers

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A Bayesian Markov chain Monte Carlo (MCMC) stochastic loss reserve model provides an arbitrarily large number of equally likely parameter sets that enable one to simulate future cash flows of the liability. Using these parameter sets to represent all future outcomes, it is possible to describe any future state in the model’s time horizon including those states necessary to calculate a cost-of-capital risk margin. This paper shows how to use the MCMC output to (1) calculate the risk margin for an “ultimate” time horizon; (2) calculate the risk margin for a one-year time horizon; and (3) analyze the effect of diversification in a risk margin calculation for multiple lines of insurance.

Keywords: Stochastic loss reserving, Bayesian MCMC, capital requirements, risk margins

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Meyers, Glenn G., "A Cost-of-Capital Risk Margin Formula for Nonlife Insurance Liabilities," Variance 12:2, 2019, pp. 186-198.

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Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.