THE SOLUTION TO A DIFFERENTIAL–DIFFERENCE EQUATION ARISING IN OPTIMAL STOPPING OF A JUMP–DIFFUSION PROCESS 2022 (English)In: RevStat: Statistical Journal, ISSN 1645-6726, Vol. 20, no 1, p. 85-100Article in journal (Refereed) Published

Abstract [en]

In this paper we present a solution to a second order differential–difference equation that occurs in different contexts, specially in control engineering and finance. This equation leads to an ordinary differential equation, whose homogeneous part is a Cauchy–Euler equation. We derive a particular solution to this equation, presenting explicitly all the coefficients. The differential–difference equation is motivated by investment decisions addressed in the context of real options. It appears when the underlying stochastic process follows a jump–diffusion process, where the diffusion is a geometric Brownian motion and the jumps are driven by a Poisson process. The solution that we present — which takes into account the geometry of the problem — can be written backwards, and therefore its analysis is easier to follow. 

Place, publisher, year, edition, pages

National Statistical Institute , 2022. Vol. 20, no 1, p. 85-100

Keywords [en]

difference equation; differential equation, jump, differential, diffusion process

National Category

Mathematics

Identifiers

URN: urn:nbn:se:ri:diva-61870DOI: 10.57805/revstat.v20i1.364Scopus ID: 2-s2.0-85143777026OAI: oai:DiVA.org:ri-61870DiVA, id: diva2:1721556

Note

Funding details: Fundação para a Ciência e a Tecnologia, FCT, 268093/E20, FARO PTDC/EGE-ECO/30535/2017, SFRH/BD/97259/2013, UID/MULTI/04621/2019; Funding text 1: Most of Rita Pimentel’s research was supported by her Ph.D. research grant from FCT with reference number SFRH/BD/97259/2013. The final part of the work was carried out during the tenure of an ERCIM ‘Alain Bensoussan’ Fellowship Programme.; Funding text 2: Most of Cláudia Nunes’s research was supported by the FCT research grants FARO PTDC/EGE-ECO/30535/2017 and UID/MULTI/04621/2019. She also acknowledge Invest ExL Project No.: 268093/E20, funded by the Norwegian research agency.

Available from: 2022-12-22 Created: 2022-12-22 Last updated: 2022-12-22Bibliographically approved

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