Consider an insurance risk model, in which the surplus process satisfies a recursive equationU n =U n?1(1+r n )?X n forn≥1, whereU 0=x≥0 is the initial surplus, {r n ;n≥1} the interest rate sequence, {X n ;n≥1} th...Consider an insurance risk model, in which the surplus process satisfies a recursive equationU n =U n?1(1+r n )?X n forn≥1, whereU 0=x≥0 is the initial surplus, {r n ;n≥1} the interest rate sequence, {X n ;n≥1} the sequence of i. i. d. real-valued random variables with common distribution functionF, which denotes the gross loss during thenth year. We investigate the ruin probability within a finite time horizon and give the asymptotic result asx→∞. Key words variable interest rate - extend regular variation - finite time ruin probability CLC number O 211.9 Foundation item: Supported by the National Natural Science Foundation of China (10071058, 70273029)Biography: WEI Xiao (1979-), female, Ph. D candidate, research direction: large deviations and its applications, insurance mathematics.展开更多
This note complements a recent study in ruin theory with risky investment byestablishing the same asymptotic estimate for the finite time ruin probability under a weakerrestriction on the financial risks. In particula...This note complements a recent study in ruin theory with risky investment byestablishing the same asymptotic estimate for the finite time ruin probability under a weakerrestriction on the financial risks. In particular, our result applies to a critical case that theinsurance and financial risks have Pareto-type tails with the same regular index.展开更多
We consider a discrete time risk model in which the net payout （insurance risk） {Xk, k = 1, 2,...} are assumed to take real values and belong to the heavy-tailed class L∩ D and the discount factors （financial risk...We consider a discrete time risk model in which the net payout （insurance risk） {Xk, k = 1, 2,...} are assumed to take real values and belong to the heavy-tailed class L∩ D and the discount factors （financial risk） {Yk, k = 1,2,...} concentrate on [θ, L], where 0 〈 0 〈 1, L 〈 ∞, {Xk, k = 1,2,...}, and {Yk, k=1,2,...} are assumed to be mutually independent. We investigate the asymptotic behavior of the ruin probability within a finite time horizon as the initial capital tends to infinity, and figure out that the convergence holds uniformly for all n ≥ 1, which is different from Tang Q H and Tsitsiashvili G （Adv Appl Prob, 2004, 36： 1278-1299）.展开更多
In this paper, we consider the finite time ruin probability for the jump-diffusion Poisson process. Under the assurnptions that the claimsizes are subexponentially distributed and that the interest force is constant, ...In this paper, we consider the finite time ruin probability for the jump-diffusion Poisson process. Under the assurnptions that the claimsizes are subexponentially distributed and that the interest force is constant, we obtain an asymptotic formula for the finite-time ruin probability. The results we obtain extends the corresponding results of Kliippelberg and Stadtmüller and Tang.展开更多
Subject to the assumption that the common distribution of claim sizes belongs to the extendedregular variation class,the present work obtains a simple asymptotic formula for the ruin probability within arandom or nonr...Subject to the assumption that the common distribution of claim sizes belongs to the extendedregular variation class,the present work obtains a simple asymptotic formula for the ruin probability within arandom or nonrandom horizon in the renewal model.展开更多
In this paper, we propose a customer-based individual risk model, in which potential claims by customers are described as i.i.d, heavy-tailed random variables, but different insurance policy holders are allowed to hav...In this paper, we propose a customer-based individual risk model, in which potential claims by customers are described as i.i.d, heavy-tailed random variables, but different insurance policy holders are allowed to have different probabilities to make actual claims. Some precise large deviation results for the prospectiveoss process are derived under certain mild assumptions, with emphasis on the case of heavy-tailed distribution function class ERV （extended regular variation）. Lundberg type limiting results on the finite time ruin probabilities are also investigated.展开更多
文摘Consider an insurance risk model, in which the surplus process satisfies a recursive equationU n =U n?1(1+r n )?X n forn≥1, whereU 0=x≥0 is the initial surplus, {r n ;n≥1} the interest rate sequence, {X n ;n≥1} the sequence of i. i. d. real-valued random variables with common distribution functionF, which denotes the gross loss during thenth year. We investigate the ruin probability within a finite time horizon and give the asymptotic result asx→∞. Key words variable interest rate - extend regular variation - finite time ruin probability CLC number O 211.9 Foundation item: Supported by the National Natural Science Foundation of China (10071058, 70273029)Biography: WEI Xiao (1979-), female, Ph. D candidate, research direction: large deviations and its applications, insurance mathematics.
文摘This note complements a recent study in ruin theory with risky investment byestablishing the same asymptotic estimate for the finite time ruin probability under a weakerrestriction on the financial risks. In particular, our result applies to a critical case that theinsurance and financial risks have Pareto-type tails with the same regular index.
基金supported by the National Natural Science Foundation of China (10671149)the Ministry of Education of China, the Natural Science Foundation of Jiangxi(2008GQS0035)the Foundation of the Hubei Provincial Department of Education (B20091107)
文摘We consider a discrete time risk model in which the net payout （insurance risk） {Xk, k = 1, 2,...} are assumed to take real values and belong to the heavy-tailed class L∩ D and the discount factors （financial risk） {Yk, k = 1,2,...} concentrate on [θ, L], where 0 〈 0 〈 1, L 〈 ∞, {Xk, k = 1,2,...}, and {Yk, k=1,2,...} are assumed to be mutually independent. We investigate the asymptotic behavior of the ruin probability within a finite time horizon as the initial capital tends to infinity, and figure out that the convergence holds uniformly for all n ≥ 1, which is different from Tang Q H and Tsitsiashvili G （Adv Appl Prob, 2004, 36： 1278-1299）.
基金Supported by the National Natural Science Foundation of China(No.70471071)Philosophy and Social Science Foundation of the Education Anthority of Jiangsu Province(No.04SJB630005)
文摘In this paper, we consider the finite time ruin probability for the jump-diffusion Poisson process. Under the assurnptions that the claimsizes are subexponentially distributed and that the interest force is constant, we obtain an asymptotic formula for the finite-time ruin probability. The results we obtain extends the corresponding results of Kliippelberg and Stadtmüller and Tang.
基金Supported by the National Statistical Science Research Project (No.LX0317)
文摘Subject to the assumption that the common distribution of claim sizes belongs to the extendedregular variation class,the present work obtains a simple asymptotic formula for the ruin probability within arandom or nonrandom horizon in the renewal model.
基金Supported by the National Natural Science Foundation of China(No.10971157)
文摘In this paper, we propose a customer-based individual risk model, in which potential claims by customers are described as i.i.d, heavy-tailed random variables, but different insurance policy holders are allowed to have different probabilities to make actual claims. Some precise large deviation results for the prospectiveoss process are derived under certain mild assumptions, with emphasis on the case of heavy-tailed distribution function class ERV （extended regular variation）. Lundberg type limiting results on the finite time ruin probabilities are also investigated.
