Minimizing or maximizing the first-passage time to a time-dependent boundary. (1st February 2022)

• Record Type: Journal Article
• Authors: Lefebvre, Mario
• Is Part Of: Optimization. Volume 71:Number 2(2022)
• Page Start: 387
• Page End: 401
• Publication Date: 2022-02-01
• Subjects: Stochastic optimal control -- game theory -- Brownian motion -- method of similarity solutions; 49N90; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1914039
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : Let X ( t ) be a one-dimensional controlled diffusion process, and Y ( t ) be a deterministic process. Various models are considered for ( X ˙ ( t ), Y ˙ ( t ) ) . The optimizer tries to bring the ratio X ( t ) / Y ( t ) to a certain value d as soon as possible. There is also a second optimizer whose aim is to prevent the ratio X ( t ) / Y ( t ) from reaching d as long as possible. Explicit solutions are obtained. The particular case when the control variables are assumed to be constants and the general case are treated.