Bayesian Risk Management for Equity-Linked Insurance

This paper describes how to apply Markov Chain Monte Carlo (MCMC) techniques to a regime switching model of the stock price process to generate a sample from the joint posterior distribution of the parameters of the model. The MCMC output can be used to generate a sample from the predictive distribution of losses from equity linked contracts, assuming first an actuarial approach to risk management and secondly a financial economics approach. The predictive distribution is used to show the effect of parameter uncertainty on risk management calculations. We also explore model uncertainty by assuming a GARCH model in place of the regime switching model. The results indicate that the financial economics approach to risk management is substantially more robust to parameter uncertainty and model uncertainty than the actuarial approach.