Optimal starting–stopping and switching of a CIR process with fixed costs

Article type: Research Article

Authors: Leung, Tim^; | Li, Xin | Wang, Zheng

Affiliations: IEOR Department, Columbia University, New York, NY, USA. E-mails: {tl2497, xl2206, zw2192}@columbia.edu

Note: [] Address for correspondence: Tim Leung, IEOR Department, Columbia University, New York, NY 10027, USA. E-mail: [email protected]

Abstract: This paper analyzes the problem of starting and stopping a Cox–Ingersoll–Ross (CIR) process with fixed costs. In addition, we also study a related optimal switching problem that involves an infinite sequence of starts and stops. We establish the conditions under which the starting–stopping and switching problems admit the same optimal starting and/or stopping strategies. We rigorously prove that the optimal starting and stopping strategies are of threshold type, and give the analytical expressions for the value functions in terms of confluent hypergeometric functions. Numerical examples are provided to illustrate the dependence of timing strategies on model parameters and transaction costs.

Keywords: Optimal starting–stopping, optimal switching, CIR process, confluent hypergeometric functions

DOI: 10.3233/RDA-140107

Journal: Risk and Decision Analysis, vol. 5, no. 2-3, pp. 149-161, 2014