Uniform Asymptotics for Discounted Aggregate Claims in Dependent Risk Models

In this paper, we consider some non-standard renewal risk models with some dependent claim sizes and stochastic return, where an insurance company is allowed to invest her/his wealth in financial assets, and the price process of the investment portfolio is described as a geometric Lévy process. When the claim-size distribution belongs to some classes of heavy-tailed distributions and a constraint is imposed on the Lévy process in terms of its Laplace exponent, we obtain some asymptotic formulas for the tail probability of discounted aggregate claims and ruin probabilities holding uniformly for some finite or infinite time horizons.

[1]  Jostein Paulsen,et al.  Risk theory in a stochastic economic environment , 1993 .

[2]  Yang Yang,et al.  Asymptotics for ruin probability of some negatively dependent risk models with a constant interest rate and dominatedly-varying-tailed claims ☆ , 2010 .

[3]  Jun Cai,et al.  Ruin probabilities and penalty functions with stochastic rates of interest , 2004 .

[4]  Kam Chuen Yuen,et al.  On the renewal risk process with stochastic interest , 2006 .

[5]  Kai W. Ng,et al.  Ruin probabilities for a risk process with stochastic return on investments , 2004 .

[6]  Moshe Shaked,et al.  Some Concepts of Negative Dependence , 1982 .

[7]  Qihe Tang,et al.  THE FINITE-TIME RUIN PROBABILITY OF THE COMPOUND POISSON MODEL WITH CONSTANT INTEREST FORCE , 2005 .

[8]  Ragnar Norberg,et al.  Power tailed ruin probabilities in the presence of risky investments , 2002 .

[9]  Qihe Tang,et al.  Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails , 2002 .

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

[11]  N. H. Bingham,et al.  Regular variation in more general settings , 1987 .

[12]  Jostein Paulsen.  On Cramér-like asymptotics for risk processes with stochastic return on investments , 2002 .

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

[14]  E. Lehmann.  Some Concepts of Dependence , 1966 .

[15]  V'ictor Rivero.  Tail asymptotics for exponential functionals of Lévy processes: The convolution equivalent case , 2009 .

[16]  Claudia Klüppelberg,et al.  Ruin probabilities in the presence of heavy tails and interest rates , 1998 .

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

[18]  K. Joag-dev,et al.  Negative Association of Random Variables with Applications , 1983 .

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

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

[21]  Vladimir Kalashnikov,et al.  Ruin under interest force and subexponential claims: a simple treatment , 2000 .

[22]  Sidney I. Resnick,et al.  Characterizations and Examples of Hidden Regular Variation , 2004 .

[23]  Qihe Tang,et al.  A uniform asymptotic estimate for discounted aggregate claims with subexponential tails , 2008 .

[24]  Qihe Tang.  Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model , 2007, Journal of Applied Probability.

[25]  Jinzhu Li.  Asymptotics in a time-dependent renewal risk model with stochastic return , 2012 .

[26]  S. Asmussen.  Subexponential asymptotics for stochastic processes : extremal behavior, stationary distributions and first passage probabilities , 1998 .

[27]  Qihe Tang,et al.  Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model , 2010 .