Dependencies in Stochastic Loss Reserve Models

By Glenn G. Meyers

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Abstract

Given a Bayesian Markov chain Monte Carlo (MCMC) stochastic loss reserve model for two separate lines of insurance, this paper describes how to fit a bivariate stochastic model that captures the dependencies between the two lines of insurance. A Bayesian MCMC model similar to the Changing Settlement Rate (CSR) model, as described in Meyers (2015), is initially fit to each line of insurance. Then taking a sample from the posterior distribution of parameters from each line, this paper shows how to produce a sample that represents a bivariate disĀ­tribution that maintains the original univariate distributions as its marginal distributions. This paper goes on to compare the predicted distribution of outcomes by this model with the actual outcomes, and a bivariate model predicted under the assumpĀ­tion that the lines are independent. It then applies two Bayesian model selection statistics to compare the fits of the two models.

Keywords: Bayesian MCMC, stochastic loss reserving, correlation, dependencies

Citation

Meyers, Glenn G., "Dependencies in Stochastic Loss Reserve Models," Variance 11:1, 2018, pp. 74-94.

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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.