Abstract
Abstract:
In this paper we develop a system of integral and differential equations forth estate wise probability distributions of the present value of future payments on a multi-states life insurance policy under semi-Markov assumptions. We also provide formulas on the probability distribution through inversion techniques on the respective moment generating functions of the present value of future payments. The results are illustrated with applications to Value-at-Risk (VaR) and TailValue-at-Risk (TVaR) calculations.