scholarly journals Finite- and Infinite-Time Ruin Probabilities with General Stochastic Investment Return Processes and Bivariate Upper Tail Independent and Heavy-Tailed Claims

2013 ◽  
Vol 45 (1) ◽  
pp. 241-273 ◽  
Author(s):  
Fenglong Guo ◽  
Dingcheng Wang
Keyword(s):  
Risk Model ◽  
Heston Model ◽  
Ruin Probabilities ◽  
Investment Risk ◽  
Insurance Risk ◽  
Infinite Time ◽  
Asymptotic Behaviors ◽  
Special Cases ◽  
Investment Returns ◽  
Heavy Tailed

In this paper we investigate the asymptotic behaviors of the finite- and infinite-time ruin probabilities for a Poisson risk model with stochastic investment returns which constitute a general adapted càdlàg process and heavy-tailed claim sizes which are bivariate upper tail independent. The results of this paper show that the asymptotic ruin probabilities are dominated by the extreme of insurance risk but not by that of investment risk. As applications of the results, we discuss four special cases when the investment returns are determined by a fractional Brownian motion, an integrated Vasicek model, an integrated Cox–Ingersoll–Ross model, and the Heston model.

scholarly journals Finite- and Infinite-Time Ruin Probabilities with General Stochastic Investment Return Processes and Bivariate Upper Tail Independent and Heavy-Tailed Claims

2013 ◽  
Vol 45 (01) ◽  
pp. 241-273 ◽  
Author(s):  
Fenglong Guo ◽  
Dingcheng Wang
Keyword(s):  
Risk Model ◽  
Heston Model ◽  
Ruin Probabilities ◽  
Investment Risk ◽  
Insurance Risk ◽  
Infinite Time ◽  
Asymptotic Behaviors ◽  
Special Cases ◽  
Investment Returns ◽  
Heavy Tailed

In this paper we investigate the asymptotic behaviors of the finite- and infinite-time ruin probabilities for a Poisson risk model with stochastic investment returns which constitute a general adapted càdlàg process and heavy-tailed claim sizes which are bivariate upper tail independent. The results of this paper show that the asymptotic ruin probabilities are dominated by the extreme of insurance risk but not by that of investment risk. As applications of the results, we discuss four special cases when the investment returns are determined by a fractional Brownian motion, an integrated Vasicek model, an integrated Cox–Ingersoll–Ross model, and the Heston model.

scholarly journals Asymptotic Behavior of Ruin Probabilities in an Insurance Risk Model with Quasi-Asymptotically Independent or Bivariate Regularly Varying-Tailed Main Claim and By-Claim

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Yang Yang ◽  
Xinzhi Wang ◽  
Xiaonan Su ◽  
Aili Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Risk Model ◽  
Dependence Structure ◽  
Ruin Probabilities ◽  
Insurance Risk ◽  
Main Claim ◽  
Regularly Varying ◽  
Heavy Tailed ◽  
Insurance Risk Model

This paper considers a by-claim risk model under the asymptotical independence or asymptotical dependence structure between each main claim and its by-claim. In the presence of heavy-tailed main claims and by-claims, we derive some asymptotic behavior for ruin probabilities.

scholarly journals Asymptotic Ruin Probabilities for a Bivariate Lévy-Driven Risk Model with Heavy-Tailed Claims and Risky Investments

2012 ◽  
Vol 49 (4) ◽  
pp. 939-953 ◽  
Author(s):  
Xuemiao Hao ◽  
Qihe Tang
Keyword(s):  
Risk Model ◽  
Moment Condition ◽  
Ruin Probabilities ◽  
Economic Factors ◽  
Infinite Time ◽  
Lévy Measure ◽  
Loss Process ◽  
Surplus Process ◽  
Heavy Tailed ◽  
Extended Regular Variation

Consider a general bivariate Lévy-driven risk model. The surplus process Y, starting with Y0=x > 0, evolves according to dYt= Yt- dRt -dPt for t > 0, where P and R are two independent Lévy processes respectively representing a loss process in a world without economic factors and a process describing the return on investments in real terms. Motivated by a conjecture of Paulsen, we study the finite-time and infinite-time ruin probabilities for the case in which the loss process P has a Lévy measure of extended regular variation and the stochastic exponential of R fulfills a moment condition. We obtain a simple and unified asymptotic formula as x→∞, which confirms Paulsen's conjecture.

Asymptotic Ruin Probabilities for a Bivariate Lévy-Driven Risk Model with Heavy-Tailed Claims and Risky Investments

2012 ◽  
Vol 49 (04) ◽  
pp. 939-953
Author(s):  
Xuemiao Hao ◽  
Qihe Tang
Keyword(s):  
Risk Model ◽  
Moment Condition ◽  
Ruin Probabilities ◽  
Economic Factors ◽  
Infinite Time ◽  
Lévy Measure ◽  
Loss Process ◽  
Surplus Process ◽  
Heavy Tailed ◽  
Extended Regular Variation

Consider a general bivariate Lévy-driven risk model. The surplus process Y, starting with Y 0=x > 0, evolves according to dY t = Y t- dR t -dP t for t > 0, where P and R are two independent Lévy processes respectively representing a loss process in a world without economic factors and a process describing the return on investments in real terms. Motivated by a conjecture of Paulsen, we study the finite-time and infinite-time ruin probabilities for the case in which the loss process P has a Lévy measure of extended regular variation and the stochastic exponential of R fulfills a moment condition. We obtain a simple and unified asymptotic formula as x→∞, which confirms Paulsen's conjecture.

scholarly journals UPPER BOUNDS FOR RUIN PROBABILITY UNDER TIME SERIES MODELS

2006 ◽  
Vol 20 (3) ◽  
pp. 529-542 ◽  
Author(s):  
Gary K. C. Chan ◽  
Hailiang Yang
Keyword(s):  
Time Series ◽  
Ruin Probability ◽  
Causal Model ◽  
Risk Model ◽  
Upper Bounds ◽  
Time Series Models ◽  
Ruin Probabilities ◽  
Insurance Risk ◽  
Special Cases ◽  
Insurance Risk Model

In this article, we consider an insurance risk model where the claim and premium processes follow some time series models. We first consider the model proposed in Gerber [2,3]; then a model with dependent structure between premium and claim processes modeled by using Granger's causal model is considered. By using some martingale arguments, Lundberg-type upper bounds for the ruin probabilities under both models are obtained. Some special cases are discussed.

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