This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with gi...This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with given initial environment state, is derived and solved. Explicit formulas for the discounted penalty function are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In two state model, numerical illustrations with exponential claim amounts are given.展开更多
In this paper, a compound Poisson risk model with time-dependent claims is studiedunder a multi-layer dividend strategy. A piecewise integro-differential equation for the Gerber- Shiu function is derived and solved. A...In this paper, a compound Poisson risk model with time-dependent claims is studiedunder a multi-layer dividend strategy. A piecewise integro-differential equation for the Gerber- Shiu function is derived and solved. Asymptotic formulas of the ruin probability are obtained when the claim size distributions are heavy-tailed.展开更多
基金supported in part by Hubei Normal University Post-graduate Foundation(2007D59 and 2007D60)the Science and Technology foundation of Hubei(D20092207)the National Natural Science Foundation of China(10671149)
文摘This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with given initial environment state, is derived and solved. Explicit formulas for the discounted penalty function are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In two state model, numerical illustrations with exponential claim amounts are given.
基金Surported by the Third Stage of 211 ProjectInnovative Talent Training Project of S-09110the Chongqing University Postgraduates’ Science and Innovation Fund (200911B1B0110327)
文摘In this paper, a compound Poisson risk model with time-dependent claims is studiedunder a multi-layer dividend strategy. A piecewise integro-differential equation for the Gerber- Shiu function is derived and solved. Asymptotic formulas of the ruin probability are obtained when the claim size distributions are heavy-tailed.
