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When an insurance company's risk reserve is governed by a Markov-modulated jump-diffusion risk model, we study gambler's ruin problem in terms of two-sided ruin probability that the insurance company shall be ruined before its risk reserve reaches an upper barrier level. We employ Banach contraction principle and  q -scale functions to confirm the two-sided ruin probability to be the only fixed point of a contraction mapping and construct an iterative algorithm of approximating the two-sided ruin probability. We find that the two-sided ruin probability and Lipschitz constant in the contraction mapping depend on the upper barrier level  b , premium rate per squared volatility, Markov intensity rate per squared volatility, Poisson intensity rate per squared volatility and the mean value of claim per unit of time. Finally, we present a numerical example with two regimes to show the efficiency of the iterative algorithm.

Gambler's ruin problem in a Markov-modulated jump-diffusion risk model