The expected discounted penalty at ruin in the risk process with random income

DOI10.1016/j.amc.2005.11.106zbMath1158.60374OpenAlexW1971702369MaRDI QIDQ849761

Zhen-Hua Bao

Publication date: 31 October 2006

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2005.11.106

zbMATH Keywords

ruin probabilitydefective renewal equationexpected discounted penalty functioncompound geometric

Mathematics Subject Classification ID

Stopping times; optimal stopping problems; gambling theory (60G40) Applications of Markov renewal processes (reliability, queueing networks, etc.) (60K20)

Related Items (22)

Risk models based on copulas for premiums and claim sizes ⋮ A ruin model with random income and dependence between claim sizes and claim intervals ⋮ The Gerber-Shiu discounted penalty function in the delayed renewal risk process with random income ⋮ Ruin under stochastic dependence between premium and claim arrivals ⋮ The compound binomial risk model with delayed claims and random income ⋮ The Gerber-Shiu discounted penalty function: a review from practical perspectives ⋮ The expected discounted penalty function under a renewal risk model with stochastic income ⋮ On a discrete Markov-modulated risk model with random premium income and delayed claims ⋮ On a class of stochastic models with two-sided jumps ⋮ On a class of renewal risk model with random income ⋮ Ruin probabilities in the risk process with random income ⋮ Gerber–Shiu function for the discrete inhomogeneous claim case ⋮ Ruin probabilities for a two-dimensional perturbed risk model with stochastic premiums ⋮ On the expected discounted penalty function and optimal dividend strategy for a risk model with random incomes and interclaim-dependent claim sizes ⋮ On a risk model with stochastic premiums income and dependence between income and loss ⋮ On a compound Poisson risk model with delayed claims and random incomes ⋮ Risk process with stochastic income and two-step premium rate ⋮ An insurance risk process with a generalized income process: a solvency analysis ⋮ Estimating the Gerber-Shiu function in a compound Poisson risk model with stochastic premium income ⋮ A Direct Approach to the Discounted Penalty Function ⋮ The expected discounted penalty function under a risk model with stochastic income ⋮ A ruin model with compound Poisson income and dependence between claim sizes and claim intervals

Cites Work

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• Calculation of the probability of eventual ruin by Beekman's convolution series
• The surpluses immediately before and at ruin, and the amount of the claim causing ruin
• Further use of Shiu's approach to the evaluation of ultimate ruin probabilities
• Aspects of risk theory
• The moments of ruin time in the classical risk model with discrete claim size distribution
• On the expected discounted penalty function at ruin of a surplus process with interest.
• Risk process with random income
• Analysis of a defective renewal equation arising in ruin theory
• On the Time Value of Ruin

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