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The Gerber-Shiu Discounted Penalty Function in the Do-uble Type-insurance Compound Binomial Risk Model with Randomized Decisions on Paying Dividend

Zhu Shuang-xi

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Abstract

In this paper,we study the double type-insurance compound binomial risk model.The insurer pays dividends to shareholders with a probability when the surplus is greater than or equal to a non-negative dividend-line.We derive the defective renewal equation and the asymptotic expressions for the Gerber-Shiu discounted penalty function by using the renewal theory.The recursion formulas and asymptotic expressions for the ruin probability,the probability function of the severity of ruin,and the surplus prior to the ruin time are obtained.

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In this paper,we study the double type-insurance compound binomial risk model.The insurer pays dividends to shareholders with a probability when the surplus is greater than or equal to a non-negative dividend-line.We derive the defective renewal equation and the asymptotic expressions for the Gerber-Shiu discounted penalty function by using the renewal theory.The recursion formulas and asymptotic expressions for the ruin probability,the probability function of the severity of ruin,and the surplus prior to the ruin time are obtained.

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Available abstract

In this paper,we study the double type-insurance compound binomial risk model.The insurer pays dividends to shareholders with a probability when the surplus is greater than or equal to a non-negative dividend-line.We derive the defective renewal equation and the asymptotic expressions for the Gerber-Shiu discounted penalty function by using the renewal theory.The recursion formulas and asymptotic expressions for the ruin probability,the probability function of the severity of ruin,and the surplus prior to the ruin time are obtained.

Key concepts: Ruin theory, Dividend, Mathematics, Penalty method, Risk model, Type (biology), Binomial distribution, Recursion (computer science)

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The Gerber-Shiu Discounted Penalty Function in the Do-uble Type-insurance Compound Binomial Risk Model with Randomized Decisions on Paying Dividend — Research Paper | ScholarLens