Reversible Jump Markov Chain Monte Carlo Method for Parameter Reduction in Claims Reserving

Abstract

We present an application of the reversible jump Markov chain Monte Carlo (RJMCMC) method to the important problem of setting claims reserves in general insurance business for the outstanding loss liabilities. A measure of the uncertainty in these claims reserves estimates is also needed for solvency purposes. The RJMCMC method described in this paper represents an improvement over the manual processes often employed in practice. In particular, our RJMCMC method describes parameter reduction and tail factor estimation in the claims reserving process, and, moreover, it provides the full predictive distribution of the outstanding loss liabilities.     

The Impact of the Automatic Balancing Mechanism for the Public Pension in Japan on the Extreme Elderly

Abstract

Most developed countries are seeking ways to maintain a sustainable social security system. Japan is no exception. The old-age dependency ratio in Japan is currently 35% and is expected to be 74% in 2050. Recently the Japanese government has adopted an automatic balancing mechanism, which gradually reduces the real price of the public pension through a reduction of inflation adjustments. The reduction, depending on future demographics, is a random process, so the elderly, in particular the extreme elderly, have to take the risk of receiving an inadequate public pension. The objectives of this paper are threefold. First, we review the recent trends in Japanese mortality and explain the underlying longevity issues that led to the automatic balancing mechanism. Second, by means of stochastic mortality and fertility modeling, we analyze how demographic changes will affect the future of public pensions in Japan. Third, we demonstrate, on the basis of the stochastic projections we made, how the automatic balancing mechanism will affect the financial security for people who live beyond age 100.