Theoretical and practical risk adjustments in an incomplete market

A new law in 2004 has been introduced that prohibits establishing the present value of a fund by the use of the age adjustment method. We aim to measure the effects of this law by computing the present value of a fund before and after an age adjustment. In incomplete markets, there is no unique risk-neutral valuation of a security. We aim to price the life insurance based on a subset of these incomplete market measures. The assets to be priced are a traded asset and the variable kt that measures the improvement in death probabilities of the insured population. We estimate their drifts and add an ambiguity region around the drift of the population by the ambiguity factor k. This will form our subset of alternative valuation measures. kt is approached by the Lee-Carter model. To approximate the death rates, we use an approach that has been found an accurate approximation in other literature. Finally, we compare the drifts of this theoretical subset model to the practice of actuaries: age adjustments and mortality experience to model longevity. We see significant differences between males, females, theoretical and practical adjustments. Just for further research to make this model closer to reality, we show how the market price of risk, the yield curve published by the DNB and the most recent Dutch mortality table AG2014 can be implemented.

Netspar, Network for Studies on Pensions, Aging and Retirement, is a thinktank and knowledge network. Netspar is dedicated to promoting a wider understanding of the economic and social implications of pensions, aging and retirement in the Netherlands and Europe.

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