Utility Indifference Valuation of Life Insurance Risks

Abstract

<p> We address the problem of valuation of life insurance risks of different nature, market independent or equity-linked, under various assumptions regarding policyholders'mortality and the financial market. Given the incomplete nature of life insurance markets, an indifference valuation approach tailored to different models of the insurer's liability is applied. To be more specific, we propose three models for the insurer's liability: a single life insurance model, the individual risk model and the collective risk model. The last two models are generalizations of the aggregate loss models with the same name from actuarial mathematics. </p> <p> First, we investigate the pricing problem of market independent life insurance risks under the assumption of random mortality, focussing on the effects of this latter assumption on the premium. We find that random mortality is an essential assumption especially when pricing in aggregate loss models. Then, we consider life insurance products with a more complex structure of the benefit, as equity-linked term life insurances. We price them via utility indifference in all liability models mentioned above, assuming deterministic mortality and a Black-Scholes market model. Comparing the results obtained, we observe that the collective risk model is computationally more efficient than the others, but at the cost of higher premium. Finally, we conclude by extend-ing our pricing results for equity-linked term life insurance to a one factor stochastic volatility market model. We obtain that in a fast-mean-reverting volatility regime, the indifference premium can be well approximated by adjusted constant volatility results, previously derived. </p>