Modelling and computation of optimal decision for farmers leasing lands

Abstract

In this paper, we use the real option theory to examine the critical factors affecting the decision of farmers to quit agriculture production and lease the land, model the optimal leasing decision as a perpetual American put option, and derive a partial differential complementary problem for the option value, which is solved by a power penalty approach. In addition, a finite difference method is employed to discretize the resulting nonlinear partial differential equation, and it is studied that when to lease the land is optimal for farmers. We also empirically compute and analyse the optimal exercise boundary to provide the assistance for the decision making and highlight the key details of the numerical implementation.

Keywords:

• real option
• partial differential complementarity problem
• power penalty approach
• finitedifference method
• convenience yield

2010 AMS Subject Classifications:

• 35Q62
• 65K15
• 91G80

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This project was supported in part by the National Basic Research Program (2012CB955804), the Major Research Plan of the National Natural Science Foundation of China (91430108), the National Natural Science Foundation of China (11171251), and the Major Program of Tianjin University of Finance and Economics.