Asymptotic ruin probabilities for proportional investment under interest force with dominatedly-varying-tailed claims

We study the asymptotic behavior of the ruin probabilities in the renewal risk model, in which the insurance company is allowed to invest a constant fraction of its wealth in a stock market which is described by a geometric Brownian motion and the remaining wealth in a bond with nonnegative interest force. We give the expression of the wealth process by the Itô formula, and finally we derive the asymptotic behavior of finite-time and infinite-time ruin probabilities in the presence of pairwise quasi-asymptotically independent claims with dominant varying tails for this model. In the particular case of compound Poisson model, explicit asymptotic expressions for the ruin probabilities are given with tails of regular variation, where the relation of the infinite-time ruin probability is the same as Gaier and Grandits (2004). For this case, we give some numerical results to assess the qualities of the asymptotic relations.