Real Options Problem with Non-Smooth Obstacle

51 Pages Posted: 18 Feb 2021

See all articles by Subas Acharya

Subas Acharya

University of Texas at Dallas - School of Natural Sciences and Mathematics

Alain Bensoussan

University of Texas at Dallas - Naveen Jindal School of Management; Hong Kong Polytechnic University - Faculty of Business; Ajou University

Dmitrii Rachinskii

University of Texas at Dallas

Alejandro Rivera

University of Texas at Dallas - School of Management - Department of Finance & Managerial Economics

Date Written: December 17, 2020

Abstract

We consider a real options problem, which is posed as a stochastic optimal control problem. The investment strategy, which plays the role of control, involves a one-time option to expand (invest) and a one-time option to abandon (terminate) the project. The timing and amount of the investment and the termination time are parameters to be optimized in order to maximize the expected value of the profit. This stochastic optimization problem amounts to solving a deterministic variational inequality in dimension one, with the associated obstacle problem. Because we consider both cessation and expansion options and fixed and variable costs of expansion, the obstacle is non-smooth. Due to the lack of smoothness, we use the concept of a weak solution. However, such solutions may not lead to a straightforward investment strategy. Therefore, we further consider strong ($C^1$) solutions based on thresholds. We propose sufficient conditions for the existence of such solutions to the variational inequality with a non-smooth obstacle in dimension one. When applied to the real options problem, these sufficient conditions yield a simple optimal investment strategy with the stopping times defined in terms of the thresholds.

Keywords: Stochastic optimal control, variational inequality, weak formulation, strong two-threshold solution, real options

Suggested Citation

Acharya, Subas and Bensoussan, Alain and Rachinskii, Dmitrii and Rivera, Alejandro, Real Options Problem with Non-Smooth Obstacle (December 17, 2020). Available at SSRN: https://ssrn.com/abstract=3751068 or http://dx.doi.org/10.2139/ssrn.3751068

Subas Acharya (Contact Author)

University of Texas at Dallas - School of Natural Sciences and Mathematics ( email )

2601 North Floyd Road
Richardson, TX 75083
United States

Alain Bensoussan

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 West Campbell Rd
SM 30
Richardson, TX 75080-3021
United States
9728836117 (Phone)

HOME PAGE: http://www.utdallas.edu/~axb046100/

Hong Kong Polytechnic University - Faculty of Business

Dept SEEM
Systems Engr * Engr Mgmt
Hong Kong, Hong Kong
China

Ajou University ( email )

Ajou
France

Dmitrii Rachinskii

University of Texas at Dallas ( email )

2601 North Floyd Road
Richardson, TX 75083
United States

Alejandro Rivera

University of Texas at Dallas - School of Management - Department of Finance & Managerial Economics ( email )

2601 North Floyd Road
P.O. Box 830688
Richardson, TX 75083
United States

HOME PAGE: http://jindal.utdallas.edu/faculty/alejandro-rivera

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
37
Abstract Views
150
PlumX Metrics