In the paper, using Levy processes subordinated by ＇asymptotically self-similar activity time＇ pro- cesses with long-range dependence, we set up new asset pricing models. Using the different construction for gamma （F） based ＇asymptotically self-similar activity time＇ processes with long-range dependence from Fin- lay and Seneta （2006） we extend the constructions for inverse-gamma and gamma based ＇asymptotically self- similar activity time＇ processes with integer-vMued parameters and long-range dependence in Heyde and Leo- nenko （2005） and Finlay and Seneta （2006） to noninteger-valued parameters.
In this study, we investigate the tail probability of the discounted aggregate claim sizes in a dependent risk model. In this model, the claim sizes are observed to follow a one-sided linear process with independent and identically distributed innovations. Investment return is described as a general stochastic process with c`adl`ag paths. In the case of heavy-tailed innovation distributions, we are able to derive some asymptotic estimates for tail probability and to provide some asymptotic upper bounds to improve the applicability of our study.
