Asymptotic ruin probability of a renewal risk model with dependent by-claims and stochastic returns

Consider a nonstandard renewal risk model, in which every main claim induces a delayed by-claim. Suppose that the surplus is invested to a portfolio of one risk-free asset and one risky asset, and the main claim sizes with by-claim sizes form a sequence of pairwise quasi-asymptotically independent random variables with dominatedly varying tails. Under this setting, asymptotic behavior of the ruin probability of this renewal risk model is investigated, by establishing a weakly asymptotic formula, as the initial surplus tends to infinity. Some numerical results are also presented to illustrate the accuracy of our asymptotic formulae.

[1]  Claudia Klüppelberg,et al.  Integrated insurance risk models with exponential Lévy investment , 2008 .

[2]  Qingwu Gao,et al.  Randomly weighted sums with dominated varying-tailed increments and application to risk theory , 2010 .

[3]  Gennady Samorodnitsky,et al.  Subexponentiality of the product of independent random variables , 1994 .

[4]  Kam Chuen Yuen,et al.  Sums of Pairwise Quasi-Asymptotically Independent Random Variables with Consistent Variation , 2009 .

[5]  Claudia Klüppelberg,et al.  Optimal Portfolios with Bounded Capital at Risk , 2001 .

[6]  Ken-iti Sato.  Lévy Processes and Infinitely Divisible Distributions , 1999 .

[7]  On pairwise quasi-asymptotically independent random variables and their applications , 2013 .

[8]  Junyi Guo,et al.  The compound binomial risk model with time-correlated claims , 2007 .

[9]  Chun Su,et al.  Approximation of the tail probability of randomly weighted sums of dependent random variables with dominated variation , 2011 .

[10]  Delay in claim settlement , 1989 .

[11]  Jostein Paulsen,et al.  Ruin theory with stochastic return on investments , 1997, Advances in Applied Probability.

[12]  K. Yuen,et al.  Ruin probabilities for time-correlated claims in the compound binomial model , 2001 .

[13]  Jostein Paulsen.  Ruin Models with Investment Income , 2008 .

[14]  Bert Zwart,et al.  Tail asymptotics for exponential function-als of L evy processes , 2006 .

[15]  PAUL EMBRECHTS,et al.  Modelling of extremal events in insurance and finance , 1994, Math. Methods Oper. Res..

[16]  Shuanming Li,et al.  On a discrete time risk model with delayed claimsand a constant dividend barrier , 2006 .

[17]  K. Ng,et al.  On ultimate ruin in a delayed-claims risk model , 2005 .

[18]  Sلأren Asmussen,et al.  Applied Probability and Queues , 1989 .

[19]  W. Feller.  One-sided Analogues of Karamata’s Regular Variation* , 2015 .

[20]  D. Applebaum.  Lévy Processes and Stochastic Calculus: Preface , 2009 .

[21]  Qihe Tang,et al.  Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tai , 2003 .

[22]  Kai Wang Ng,et al.  The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims , 2007 .

[23]  C. C. Heyde,et al.  Finite-time ruin probability with an exponential Lévy process investment return and heavy-tailed claims , 2009, Advances in Applied Probability.

[24]  R. Cont,et al.  Financial Modelling with Jump Processes , 2003 .

[25]  H. Waters,et al.  Ruin probabilities allowing for delay in claims settlement , 1985 .

[26]  Claudia Klüppelberg,et al.  Optimal portfolios when stock prices follow an exponential Lévy process , 2004, Finance Stochastics.