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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.