Upper bounds for ruin probabilities under stochastic interest rate and optimal investment strategies

In this paper, we study the upper bounds for ruin probabilities of an insurance company which invests its wealth in a stock and a bond. We assume that the interest rate of the bond is stochastic and it is described by a Cox-Ingersoll-Ross (CIR) model. For the stock price process, we consider both the case of constant volatility (driven by an O-U process) and the case of stochastic volatility (driven by a CIR model). In each case, under certain conditions, we obtain the minimal upper bound for ruin probability as well as the corresponding optimal investment strategy by a pure probabilistic method.