Computation of Life Insurance Reserves under Fractional Hull-White Interest Rates

Abstract

Hull-White interest rate models driven by fractional Brownian motion with Hurst parameter H not equal to 1/2 is applied to life insurance policies. The theory of life insurance policies under stochastic interest rates is thus generalized to a wider class of interest rate models. Utilizing the theory of markets with small proportional transaction costs, where it is possible to avoid arbitrage even when the market noise is driven by fractional Brownian motion, we derive formulas for the reserves of life insurance policies under fractional Hull-White interest rates. Single premiums for a theoretical pension policy under a fractional Vasicek model is computed and a sensitivity analysis is carried out. The results of the analysis suggests that persistence in the interest rates might increase the single premiums substantially and thus prose a threat to a insurance company's solvency.