| Nowadays,the relationships among different risk elements in insurance companies are getting increasingly close and complex because of the opening of the insurance market and insurance product diversification.The traditional risk models usually assume that these risk elements are independent,which leads to underestimate or overestimate the ruin probability and make bad decisions for capital allocation.On the basis of the existing research,this dissertation considers the asymptotic behaviors of ruin probabilities for risk models with heavy-tailed claims and ore dependent structures.In addition,we apply the obtained results to some related capital allocation problems.The main jobs and innovations of the dissertation are as follows:Considering the interplay of insurance market and financial market,we propose a discrete-time risk model with insurance and financial risks which are equipped with a dependence structure of regression type.Based on some results on tail behavior for random weighted sums,we investigate the tail behaviors for the ruin probabilities.We obtain a precise asymptotic relationship for the ruin probability when the common claim-size distribution has a dominated varying tail.In particular,the corresponding estimate is proved to be hold uniformly for the time horizon when the claims are regularly varying.Using the obtained results,we study the optimal strategy of maximizing the expected wealth under a constraint on the ruin probability.Taking into account the interaction between claims from two different lines,we investigate a bidimensional renewal risk model with simultaneous arrivals and dependent subexponential claims.Assuming that the claim size vectors form a sequence of independent and identically distributed random vectors with common bivariate Farlie-Gumbel-Morgenstern distribution,we derive a general asymptotic result for the finite-time ruin probability,which quantitatively captures the impact of dependence structure.Using the obtained result,we show how the insurer allocates initial capital between two different lines to minimize the ruin probability.In regard to the inconsistency of claim arrival processes of two different lines,we propose a bidimensional renewal risk model with a constant force of interest and non-simultaneous arrivals.In this risk model,the two claim-number processes are arbitrarily dependent.When the claims from different lines are independent,we derived a simple asymptotic relation for the finite-time ruin probability under the assumption that the claims are subexponential.When the claim from different lines are dependent,we describe the dependent structure by a wide type of copulas and establish an explicit asymptotic formula for the finite-time ruin probability under the assumption that the claims belong to regularly varying class which is an important subclass of the subexponential class.Using the obtained formulas,we also consider a capital allocation problem.The result shows that dependence structure will affect the selection of capital allocation strategies. |
