Optimal Starting-Stopping and Switching of a CIR Process with Fixed Costs

Risk and Decision Analysis, Volume 5, Number 2-3, pp.149-161, 2014

20 Pages Posted: 1 Oct 2014 Last revised: 31 Dec 2017

See all articles by Tim Leung

Tim Leung

University of Washington - Department of Applied Math

Xin Li

Columbia University

Zheng Wang

Columbia University

Date Written: November 24, 2014

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

JEL Classification: C41, G11, G12

Suggested Citation

Leung, Tim and Li, Xin and Wang, Zheng, Optimal Starting-Stopping and Switching of a CIR Process with Fixed Costs (November 24, 2014). Risk and Decision Analysis, Volume 5, Number 2-3, pp.149-161, 2014, Available at SSRN: https://ssrn.com/abstract=2503440 or http://dx.doi.org/10.2139/ssrn.2503440

Tim Leung (Contact Author)

University of Washington - Department of Applied Math ( email )

Lewis Hall 217
Department of Applied Math
Seattle, WA 98195
United States

HOME PAGE: http://faculty.washington.edu/timleung/

Xin Li

Columbia University ( email )

345 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

HOME PAGE: http://www.columbia.edu/~xl2206/

Zheng Wang

Columbia University ( email )

345 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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