The famous Embrechts-Goldie-Veraverbeke formula shows that, in the classical Cramér-Lundberg risk model, the ruin probabilities satisfy $R(x, \infty ) \sim \rho ^{ - 1} \bar F_e (x)$ if the claim sizes are heavy-...The famous Embrechts-Goldie-Veraverbeke formula shows that, in the classical Cramér-Lundberg risk model, the ruin probabilities satisfy $R(x, \infty ) \sim \rho ^{ - 1} \bar F_e (x)$ if the claim sizes are heavy-tailed, where Fe denotes the equilibrium distribution of the common d.f. F of the i.i.d. claims, ? is the safety loading coefficient of the model and the limit process is for x → ∞. In this paper we obtain a related local asymptotic relationship for the ruin probabilities. In doing this we establish two lemmas regarding the n-fold convolution of subexponential equilibrium distributions, which are of significance on their own right.展开更多
In this paper, we give a result on the local asymptotic behaviour of the probability of ruin in a continuous-time risk model in which the inter-claim times have an Erlang distribution and the individual claim sizes ha...In this paper, we give a result on the local asymptotic behaviour of the probability of ruin in a continuous-time risk model in which the inter-claim times have an Erlang distribution and the individual claim sizes have a distribution that belongs to S(v) with v ≥ 0, but where the Lundberg exponent of the underlying risk process does not exist.展开更多
基金Supported in part by the National Natural Science Foundation of China(10971157)the Fundamental Research Funds for the Central Universities of China(201274360)
基金Supported by the National Natural Science Foundation of China(11771343,11601097)the Science and Technology Research Project of Jiangxi Provincial Education Department(GJJ180201,GJJ150401)
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10071081).
文摘The famous Embrechts-Goldie-Veraverbeke formula shows that, in the classical Cramér-Lundberg risk model, the ruin probabilities satisfy $R(x, \infty ) \sim \rho ^{ - 1} \bar F_e (x)$ if the claim sizes are heavy-tailed, where Fe denotes the equilibrium distribution of the common d.f. F of the i.i.d. claims, ? is the safety loading coefficient of the model and the limit process is for x → ∞. In this paper we obtain a related local asymptotic relationship for the ruin probabilities. In doing this we establish two lemmas regarding the n-fold convolution of subexponential equilibrium distributions, which are of significance on their own right.
基金This work was supported by the National Natural Science Foundation of China(Grant No.19801020).
文摘In this paper, we give a result on the local asymptotic behaviour of the probability of ruin in a continuous-time risk model in which the inter-claim times have an Erlang distribution and the individual claim sizes have a distribution that belongs to S(v) with v ≥ 0, but where the Lundberg exponent of the underlying risk process does not exist.
