Exact solutions to the homing problem for a Wiener process with jumps. (1st February 2021)

• Record Type: Journal Article
• Authors: Lefebvre, Mario; Moutassim, Abderrazak
• Is Part Of: Optimization. Volume 70:Number 2(2021)
• Page Start: 307
• Page End: 319
• Publication Date: 2021-02-01
• Subjects: Brownian motion -- Poisson process -- first-passage time -- optimal stochastic control -- differential-difference equation; 93E20; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1711084
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : We consider the problem of optimally controlling a one-dimensional Wiener process with Poissonian jumps until it leaves the interval [ a, b ] . The exact optimal control is obtained in a particular case by solving the differential-difference equation satisfied by the value function. An approximate solution is also presented in a more general case. This approximate solution is appropriate when the jump size is small.