Exponential behavior in the presence of dependence in risk theory

We consider an insurance portfolio situation in which there is possible dependence between the waiting time for a claim and its actual size. By employing the underlying random walk structure we obtain explicit exponential estimates for infinite- and finite-time ruin probabilities in the case of light-tailed claim sizes. The results are illustrated in several examples, worked out for specific dependence structures.

[1]  Bill Ravens,et al.  An Introduction to Copulas , 2000, Technometrics.

[2]  Søren Asmussen,et al.  Ruin probabilities , 2001, Advanced series on statistical science and applied probability.

[3]  S. Asmussen.  Conditioned limit theorems relating a random walk to its associate, with applications to risk reserve processes and the GI/G/ 1 queue , 1982 .

[4]  W. Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[5]  D. V. Widder,et al.  The Laplace Transform , 1943 .

[6]  William Feller,et al.  An Introduction to Probability Theory and Its Applications, Vol. 2 , 1967 .

[7]  Satishs Iyengar,et al.  Multivariate Models and Dependence Concepts , 1998 .

[8]  Charles M. Grinstead,et al.  Introduction to probability , 1986, Statistics for the Behavioural Sciences.

[9]  Tomasz Rolski,et al.  Stochastic Processes for Insurance and Finance , 2001 .

[10]  R. Strawderman.  Continuous Multivariate Distributions, Volume 1: Models and Applications , 2001 .

[11]  G. Isac.  Models and applications , 1992 .

[12]  W. Feller,et al.  An Introduction to Probability Theory and its Applications, Vol. II , 1967 .

[13]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[14]  Paul Embrechts,et al.  Stochastic processes in insurance and finance , 2001 .

[15]  J. Teugels,et al.  The exponential rate of convergence of the distribution of the maximum of a random walk. Part II , 1975 .

[16]  C. Genest,et al.  Statistical Inference Procedures for Bivariate Archimedean Copulas , 1993 .

[17]  Some asymptotic results for transient random walks with applications to insurance risk , 2001, Journal of Applied Probability.

[18]  Edmund Taylor Whittaker,et al.  A Course of Modern Analysis , 2021 .