Probability of ruin of insurance company plays an important role for its shareholders and regulators. Classical risk theory describes evolution of wealth or surplus with Cramér-Lundberg process. Scale functions and their characteristics will be presented in this work as well as their use in one-sided and two-sided exit problems. Scale functions will also be applied in Gerber-Shiu risk theory for classical risk process. Time of ruin, deficit at ruin and surplus prior to ruin will be analysed with Gerber-Shiu risk theory. Classical theory will be upgraded with three path perturbations, which can translate to dividend and tax policies in insurance. In these strategies probability of ruin and expected present value of payouts (dividends or taxes) until ruin will be computed.
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