A system of non-local parabolic PDE and application to option pricing. Issue 5 (2nd September 2016)

• Record Type: Journal Article
• Authors: Goswami, Anindya; Patel, Jeeten; Shevgaonkar, Poorva
• Is Part Of: Stochastic analysis and applications. Volume 34:Issue 5(2016)
• Page Start: 893
• Page End: 905
• Publication Date: 2016-09-02
• Subjects: Semi-Markov processes -- Volterra integral equation -- non-local parabolic PDE -- locally risk minimizing pricing -- optimal hedging; 60K15 -- 91B30 -- 91G20 -- 91G60; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2016.1189340
• Languages: English
• ISSNs: 0736-2994

Abstract

ABSTRACT: This article includes a proof of well posedness of an initial-boundary value problem involving a system of non-local parabolic partial differential equation (PDE), which naturally arises in the study of derivative pricing in a generalized market model, which is known as a semi-Markov modulated geometric Brownian motion (GBM) model We study the well posedness of the problem via a Volterra integral equation of second kind. A probabilistic approach, in particular the method of conditioning on stopping times is used for showing the uniqueness.