Building Prospective Life Tables for small size datasets: Measuring systematic risks using a Monte-Carlo simulation approach

Resumo/Abstract: In pricing and calculating the best estimate of technical provisions life insurance companies and pension funds shall make use of and be consistent with information provided by the financial markets and generally available data on underwriting risks. The calculation of the best estimate shall be based upon up-to-date and credible information and realistic assumptions and be performed using adequate, applicable and relevant actuarial and statistical methods. Managing underwriting risks involves measuring risk exposure and determining the premiums that needs to be charged to insure that risk. To measure underwriting risks each insurance company has its own set of underwriting guidelines to help the underwriter determine whether or not the company should accept the risk and measure its significance. Because of this, companies should build prospective life tables considering the particularities of its own portfolio. This process has many practical difficulties, among them the fact that the volume of available data is normally limited and with a limited time range, usually no longer than a decade. Because of this, we need to resort relational methods, i.e., to mathematical expressions which relates mortality behaviour in a population where there is poor mortality data, to that of a population that is known to have sufficient or reliable data. Life tables estimated like this entail an estimation risk that adds uncertainty to the level of best estimate technical provisions to set up. The best estimate shall allow for uncertainty in the future cash-flows used for the calculation. In this paper we develop a method to measure the systematic risks in estimating prospective life tables for small size datasets using a Monte-Carlo simulation approach. The method provides us with confidence intervals for the best estimate that carry information on the variability of the cash flows necessary to ensure that the best estimate represents the mean of the cash flows.

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