Average‐tempered stable subordinators with applications

Abstract

AbstractIn this article, the running average of a subordinator with a tempered stable distribution is considered. We investigate a family of previously unexplored infinite‐activity subordinators induced by the probability distribution of the running average process and determine their jump intensity measures. Special cases including gamma processes and inverse Gaussian processes are discussed. Then we derive easily implementable formulas for the distribution functions, cumulants, and moments, as well as provide explicit estimates for their asymptotic behaviors. Numerical experiments are conducted for illustrating the applicability and efficiency of the proposed formulas. Two important extensions of the running average process and its equi‐distributed subordinator are subsequently examined, with concrete applications to structural degradation modeling with memory and financial derivatives pricing in the presence of enhanced asymmetric leptokurtic feature, where their advantages relative to various existing models are highlighted together with the mention of Euler discretization and compound Poisson approximation techniques.