Consider two dependent renewal risk models with constant interest rate. By using some methods in the risk theory, uniform asymptotics for finite-time ruin probability is derived in a non-compound risk model, where cla...Consider two dependent renewal risk models with constant interest rate. By using some methods in the risk theory, uniform asymptotics for finite-time ruin probability is derived in a non-compound risk model, where claim sizes are upper tail asymptotically independent random variables with dominatedly varying tails, claim inter-arrival times follow the widely lower orthant dependent structure, and the total amount of premiums is a nonnegative stochastic process. Based on the obtained result, using the method of analysis for the tail probability of random sums, a similar result in a more complex and reasonable compound risk model is also obtained, where individual claim sizes are specialized to be extended negatively dependent and accident inter-arrival times are still widely lower orthant dependent, and both the claim sizes and the claim number have dominatedly varying tails.展开更多
This paper studies the optimization problem with both investment and proportional reinsurance control under the assumption that the surplus process of an insurance entity is represented by a pure diffusion process.The...This paper studies the optimization problem with both investment and proportional reinsurance control under the assumption that the surplus process of an insurance entity is represented by a pure diffusion process.The company can buy proportional reinsurance and invest its surplus into a Black-Scholes risky asset and a risk free asset without restrictions.The authors define absolute ruin as that the liminf of the surplus process is negative infinity and propose absolute ruin minimization as the optimization scenario.Applying the HJB method the authors obtain explicit expressions for the minimal absolute ruin function and the associated optimal investment strategy.The authors find that the minimal absolute ruin function here is convex,but not S-shaped investigated by Luo and Taksar(2011).And finally,from behavioral finance point of view,the authors come to the conclusion:It is the restrictions on investment that results in the kink of minimal absolute ruin function.展开更多
This paper considers the nonstandard renewal risk model in which a part of surplus is invested into a Black-Scholes market whose price process is modelled by a geometric Brownian motion, claim sizes form a sequence of...This paper considers the nonstandard renewal risk model in which a part of surplus is invested into a Black-Scholes market whose price process is modelled by a geometric Brownian motion, claim sizes form a sequence of not necessarily identically distributed and pairwise quasi-asymptotically independent random variables with dominatedly-varying tails.The authors obtain a weakly asymptotic formula for the finite-time and infinite-time ruin probabilities.In particular,if the claims are identically distributed and consistently-varying tailed,then an asymptotic formula is presented.展开更多
This paper studies the complete monotonicity of the probability of ruin in the the classical risk model and the classical risk model that is perturbed by a diffusion. As a byproduct, the authors give an alternative p...This paper studies the complete monotonicity of the probability of ruin in the the classical risk model and the classical risk model that is perturbed by a diffusion. As a byproduct, the authors give an alternative proof to a result on the optimal dividend problem due to Loeffen （2008）.展开更多
This paper establishes some asymptotic formulas for the infinite-time ruin probabilities of two kinds of dependent risk models. One risk model considers the claim sizes as a modulated process, and the other deals with...This paper establishes some asymptotic formulas for the infinite-time ruin probabilities of two kinds of dependent risk models. One risk model considers the claim sizes as a modulated process, and the other deals with negatively upper orthant dependent claim sizes. In the two models, the inter-arrival times are both assumed to be negatively lower orthant dependent.展开更多
基金The National Natural Science Foundation of China(No.11001052,11171065,71171046)China Postdoctoral Science Foundation(No.2012M520964)+1 种基金the Natural Science Foundation of Jiangsu Province(No.BK20131339)the Qing Lan Project of Jiangsu Province
文摘Consider two dependent renewal risk models with constant interest rate. By using some methods in the risk theory, uniform asymptotics for finite-time ruin probability is derived in a non-compound risk model, where claim sizes are upper tail asymptotically independent random variables with dominatedly varying tails, claim inter-arrival times follow the widely lower orthant dependent structure, and the total amount of premiums is a nonnegative stochastic process. Based on the obtained result, using the method of analysis for the tail probability of random sums, a similar result in a more complex and reasonable compound risk model is also obtained, where individual claim sizes are specialized to be extended negatively dependent and accident inter-arrival times are still widely lower orthant dependent, and both the claim sizes and the claim number have dominatedly varying tails.
基金supported by the National Natural Science Foundation for Young Scholars of China under Grant No.11401556the National Natural Science Foundation of China under Grant Nos.11471304 and 11171321
文摘This paper studies the optimization problem with both investment and proportional reinsurance control under the assumption that the surplus process of an insurance entity is represented by a pure diffusion process.The company can buy proportional reinsurance and invest its surplus into a Black-Scholes risky asset and a risk free asset without restrictions.The authors define absolute ruin as that the liminf of the surplus process is negative infinity and propose absolute ruin minimization as the optimization scenario.Applying the HJB method the authors obtain explicit expressions for the minimal absolute ruin function and the associated optimal investment strategy.The authors find that the minimal absolute ruin function here is convex,but not S-shaped investigated by Luo and Taksar(2011).And finally,from behavioral finance point of view,the authors come to the conclusion:It is the restrictions on investment that results in the kink of minimal absolute ruin function.
基金supported by the National Science Foundation of China under Grant No.11071182the fund of Nanjing University of Information Science and Technology under Grant No.Y627
文摘This paper considers the nonstandard renewal risk model in which a part of surplus is invested into a Black-Scholes market whose price process is modelled by a geometric Brownian motion, claim sizes form a sequence of not necessarily identically distributed and pairwise quasi-asymptotically independent random variables with dominatedly-varying tails.The authors obtain a weakly asymptotic formula for the finite-time and infinite-time ruin probabilities.In particular,if the claims are identically distributed and consistently-varying tailed,then an asymptotic formula is presented.
基金supported by the National Natural Science Foundation of China under Grant No.11171179the Research Fund for the Doctoral Program of Higher Education of China under Grant No.20093705110002
文摘This paper studies the complete monotonicity of the probability of ruin in the the classical risk model and the classical risk model that is perturbed by a diffusion. As a byproduct, the authors give an alternative proof to a result on the optimal dividend problem due to Loeffen （2008）.
基金This research is supported by National Science Foundation of China under Grant No. 10671139 and the Science Foundation of Jiangsu Province under Grant No. 11071182.
文摘This paper establishes some asymptotic formulas for the infinite-time ruin probabilities of two kinds of dependent risk models. One risk model considers the claim sizes as a modulated process, and the other deals with negatively upper orthant dependent claim sizes. In the two models, the inter-arrival times are both assumed to be negatively lower orthant dependent.
