Reversible Jump Markov Chain Monte Carlo method

Document description

Calculating deterministic reserves is no longer sufficient in our times of enhanced Risk Management. Today, Insurers strive to have a complete view of the risk underlying reserves valuation: therefore stochastic projection methods become central to today’s actuaries.

It is even more the case with the Solvency II European Regulation which requires a VaR99.5% valuation… and consequently a very robust stochastic model to obtain a credible tail valuation.

This paper presents an innovative application of the Reversible Jump Markov Chain Monte Carlo (RJMCMC) new stochastic method.

How reliable is this new approach? The paper will provide some checks based on actual insurers’ data, and compare with the results of other commonly used methodologies.

It appears that the advantages of the method are many: in particular it does not require minimum Chain Ladder assumptions, and it is the first to enable automated definition of zones within the triangle where different models will be automatically defined to better adjust to the quantity of data available.

Some new extensions to the original RJMCMC method will also be explored in the article: for example the use of other tail or “right triangle” distribution functions as well as different time horizons, along with a methodology to choose the most suitable ones; and the estimation of the one-year uncertainty to compare RJMCMC with traditional one-year horizon methods and in particular in the context of the Solvency II framework.