A renewal theory approach to two-state switching problems with infinite values. (March 2020)

• Record Type: Journal Article
• Authors: Ekström, Erik; Olofsson, Marcus; Vannestål, Martin
• Is Part Of: Journal of applied probability. Volume 57:Number 1(2020)
• Page Start: 1
• Page End: 18
• Publication Date: 2020-03
• Subjects: Optimal switching, -- renewal theory, -- expected growth rate, -- trend following; 60K05, -- 93E20, -- 62L15, -- 91G10; 519.2
• DOI: 10.1017/jpr.2019.74
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract: We study a renewal theory approach to perpetual two-state switching problems with infinite value functions. Since the corresponding value functions are infinite, the problems fall outside the standard class of problems which can be analyzed using dynamic programming. Instead, we propose an alternative formulation of optimal switching theory in which optimality of a strategy is defined in terms of its long-term mean return, which can be determined using renewal theory. The approach is illustrated by examples in connection with trend-following strategies in finance.