On the construction of non-affine jump-diffusion models. Issue 5 (3rd September 2017)

• Record Type: Journal Article
• Authors: Gapeev, Pavel V.; Stoev, Yavor I.
• Is Part Of: Stochastic analysis and applications. Volume 35:Issue 5(2017)
• Page Start: 900
• Page End: 918
• Publication Date: 2017-09-03
• Subjects: Stochastic differential equations -- jump-diffusion processes -- non-affine processes -- market price of risk; Primary 60J75 -- 60H10 -- 91G30 -- Secondary 60J60 -- 60G51 -- 60G44; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2017.1333008
• Languages: English
• ISSNs: 0736-2994

Abstract

ABSTRACT: We describe a method for construction of jump analogues of certain one-dimensional diffusion processes satisfying solvable stochastic differential equations. The method is based on the reduction of the original stochastic differential equations to the ones with linear diffusion coefficients, which are reducible to the associated ordinary differential equations, by using the appropriate integrating factor processes. The analogues are constructed by means of adding the jump components linearly into the reduced stochastic differential equations. We illustrate the method by constructing jump analogues of several diffusion processes and expand the notion of market price of risk to the resulting non-affine jump-diffusion models.