scholarly journals Asymptotics for the Tail Behavior of Total Claims for a Risk Model with Stochastic Returns

2018 ◽  
Author(s):  
Yinghua Dong
Keyword(s):  
Risk Model ◽  
Tail Behavior ◽  
Stochastic Returns

A necessary and sufficient condition for the subexponentiality of the product convolution

2018 ◽  
Vol 50 (01) ◽  
pp. 57-73 ◽  
Author(s):  
Hui Xu ◽  
Fengyang Cheng ◽  
Yuebao Wang ◽  
Dongya Cheng
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Sufficient Conditions ◽  
Related Result ◽  
Sufficient Condition ◽  
Insurance Risk ◽  
Necessary And Sufficient Condition ◽  
Long Tail ◽  
Stochastic Returns ◽  
Necessary And Sufficient

Abstract Let X and Y be two independent and nonnegative random variables with corresponding distributions F and G. Denote by H the distribution of the product XY, called the product convolution of F and G. Cline and Samorodnitsky (1994) proposed sufficient conditions for H to be subexponential, given the subexponentiality of F. Relying on a related result of Tang (2008) on the long-tail of the product convolution, we obtain a necessary and sufficient condition for the subexponentiality of H, given that of F. We also study the reverse problem and obtain sufficient conditions for the subexponentiality of F, given that of H. Finally, we apply the obtained results to the asymptotic study of the ruin probability in a discrete-time insurance risk model with stochastic returns.

On corrected phase-type approximations of the time value of ruin with heavy tails

2019 ◽  
Vol 36 (1-4) ◽  
pp. 57-75
Author(s):  
Daniel J. Geiger ◽  
Akim Adekpedjou
Keyword(s):  
Heavy Tails ◽  
Risk Model ◽  
Correction Term ◽  
Classical Case ◽  
Penalty Functions ◽  
Tail Behavior ◽  
Time Value ◽  
Phase Type ◽  
Heavy Tailed ◽  
Relative Errors

Abstract We approximate Gerber–Shiu functions with heavy-tailed claims in a recently introduced risk model having both interclaim times and premiums depending on the claim sizes. We apply a technique known as “corrected phase-type approximations”. This results in adding a correction term to the Gerber–Shiu function with phase-type claim sizes. The correction term contains the heavy-tailed behavior at most once per convolution and captures the tail behavior of the true Gerber–Shiu function. We make the tail behavior specific in the classical case of one class of risk insured. After illustrating a use of such approximations, we study numerically the approximations’ relative errors for some specific penalty functions and claims distributions.

scholarly journals A Note on the Tail Behavior of Randomly Weighted Sums with Convolution-Equivalently Distributed Random Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Yang Yang ◽  
Jun-feng Liu ◽  
Yu-lin Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Discrete Time ◽  
Finite Time ◽  
Risk Model ◽  
Random Variables ◽  
Weighted Sums ◽  
Financial Risks ◽  
Tail Behavior ◽  
Insurance Risk ◽  
Randomly Weighted Sums

We investigate the tailed asymptotic behavior of the randomly weighted sums with increments with convolution-equivalent distributions. Our obtained result can be directly applied to a discrete-time insurance risk model with insurance and financial risks and derive the asymptotics for the finite-time probability of the above risk model.

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