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Retrospective and Prospective Liabilities, Probabilistic and Stochastic Process in Discrete Time for a policy portfolio (I)
This paper is an extension of the “Insurance Risk with Markov Chain Monte Carlo (MCMC) and Method of Moments (MM)”, the method is applied to a portfolio of insurance policies with guaranteed profitability and surrender option. Retrospective valuation is associated with the debt that is reported to the policyholder by the insurer. On the other hand, the insurer performs the prospective valuation of the cash flow that must be discounted with a yield curve, and which must contain the surrender option by the insured. For discrete-time stochastic scenarios, it is feasible to determine the structure of the probability distribution of future flows, which is not necessarily a normal distribution. It will be demonstrated by MM that for insurance with a surrender option, such as endowment or whole life, the expectation of future flows E(BEL) and its respective future variance V(BEL), can be obtained, both in present value, and as a consequence, calculate the contractual insurance margin (MCS) of the insurer. It will also be shown that by MCMC the convergence of the mean (BEL) and sample variance σ^2 (BEL), the probability distribution of future (MCS) flows will be graphed in 2 and 3 dimensions as a function of time. Likewise, it will be demonstrated that there is no single scalar statistic that, when multiplied by the σ(BEL) standard deviation, results in a standardized risk adjustment.
May 21, 2025