Optimal pricing barriers in a regulated market using reflected diffusion processes. Issue 4 (2nd April 2016)

• Record Type: Journal Article
• Authors: Han, Zheng; Hu, Yaozhong; Lee, Chihoon
• Is Part Of: Quantitative finance. Volume 16:Issue 4(2016)
• Page Start: 639
• Page End: 647
• Publication Date: 2016-04-02
• Subjects: Reflected stochastic differential equations -- Regulated (controlled) market -- Optimal barriers -- Ergodic cost -- Infinite horizon discount cost; Primary: 62L12 -- Secondary: 62M05; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2015.1034163
• Languages: English
• ISSNs: 1469-7688

Abstract

Abstract : We consider a class of one-dimensional (1D) reflected stochastic differential equations (SDEs). Such reflected SDE models arise as the key approximating processes in a regulated financial market system, and our main goal is to determine the set of optimal pricing barriers. We consider the running cost associated with the deviation of the process from the desired target level, and also the control cost from the interventions in an effort to keep the process inside the boundaries. Both a long-time average (ergodic) cost criterion and an infinite horizon discount cost criterion, where the discount factor is allowed to vary from one period to another, are studied, with numerical examples illustrating our main results.