Ruin Probabilities and Investment Under Interest Force in the Presence of Regularly Varying Tails

This paper consists of three parts. In the first part we derive the asymptotic behavior of the optimal ruin probability of an insurer who invests optimally in a stock in the presence of positive interest force and claims with tails of regular variation. Our results extend previously obtained results by Gaier & Grandits (2002) with zero interest, and by Klüppelberg & Stadtmüller (1998) without investment possibility. In the second part we prove an existence theorem for the integro-differential equation for the survival probability of an insurer, who invests a constant fraction of his wealth in a risky stock, and his remaining wealth in a bond with nonnegative interest. Our result extends a previously known result by Wang & Wu (2001). Finally, in the third part we derive the asymptotic behavior of the ruin probability of the insurer, introduced in the second part, in the presence of claims with tails of regular variation. Keywords: Ruin Probabilities, Regular Variation, Optimal Investment, Proportional Investment, Interest Force