Ruin under Light-Tailed or Moderately Heavy-Tailed Insurance Risks Interplayed with Financial Risks

Consider an insurer who makes risk-free or risky investments and hence is exposed to both insurance and financial risks. We investigate the interplay of the two risks in causing ruin of the insurer and for this purpose we describe the insurer’s business by a discrete-time model with the insurance and financial risks forming a sequence of independent and identically distributed pairs with a generic random pair (X, Y). Assuming that the pair (X, Y) follows a Sarmanov distribution with the marginal of X light-tailed or moderately heavy-tailed, we derive some asymptotic formulas for the ruin probability for various scenarios of financial risks. Intensive numerical studies are conducted to illustrate the necessity of using light-tailed or moderately heavy-tailed distributions in a given situation and to examine the accuracy of the obtained asymptotic estimates for the ruin probability.