On inverse-Gamma distribution delayed by Poisson process

Abstract

The models of stochastic subordination, or random time indexing, has been recently applied to model financial returns series X(t)t≥0 exhibiting sharp, and large variations. These sharp and large variations are linked to information arrivals and/or represent sudden events, and hence we have a model with jumps. For this purpose, by substituting the usual deterministic time t as a subordinator T(t)t≥0 in a stochastic process X(t)t≥0 we obtain a new process X(T(t))t≥0 whose stochastic time is dominated by the subordinator T(t)t≥0. Therefore, we propose in this paper an alternative approach based on a combination of the continuous-time bilinear (COBL) process subordinated by a Poisson process (that it is a Levy process) which permits us to introduce further randomness for the phenomena which exhibit either a speeded up or slowed down behavior. So, the main probabilistic properties of such models are studied and the explicit expression of the higher-order moments properties are given.