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

Asymptotic Behavior of Ruin Probabilities in an Insurance Risk Model with Quasi‐Asymptotically Independent or Bivariate Regularly Varying‐Tailed Main Claim and By‐Claim

“…Li [15] considered a dependent by-claim risk model with positive interest rate and extendedly varying tailed main claims and by-claims under the pairwise quasi-asymptotical independence structure (see the definition below). Fu and Li [16] further generalized Li's result by allowing the insurance company to invest its surplus into a portfolio consisting of risk-free and risky assets. Recently, Li [17] studied a by-claim risk model with no interest rate under the setting that each pair of the main claim and by-claim follows the asymptotical independence structure or possesses a bivariate regularly varying tail (hence, follows the asymptotical dependence structure).…”

Asymptotics for ultimate ruin probability in a by-claim risk model

“…In the study of dependent by-claim risk models with positive interest rate, [13] considered the case that all main claims and by-claims are pairwise quasi-asymptotically independent and established an asymptotic formula for the ultimate http://www.journals.vu.lt/nonlinear-analysis ruin probability. Based on [8], the paper [13] further studied a dependent renewal risk model with stochastic returns by allowing an insurer to invest its surplus into a portfolio consisting of risk-free and risky assets. For more recent advances in dependent (by-claim) risk models with interest rate, one can be referred to [2,4,9,12,15,[23][24][25][26]28], among others.…”

Finite-time ruin probability of a perturbed risk model with dependent main and delayed claims

“…In the presence of heavy-tailed claims, [15] studied the model with two deterministic linear functions for the premium income process and the stochastic accumulated return rate process (i.e., c(t) = c and R t = rt for premium rate c > 0 and interest rate r > 0); [16] considered the case of c(t) = c and R t = 0; and both of these two literatures derived the asymptotic relation for ψ(x). A few extensions with dependence structures and stochastic returns can be found in [9][10][11]27], who investigated the asymptotic behavior for both ψ(x; t) and ψ(x). Some related results in bidimensional risk models can be found in [2,3,26], among others.…”