A full balance sheet two-mode optimal switching problem

Abstract

We formulate and solve a finite horizon full balance sheet of a two-mode optimal switching problem related to trade-off strategies between expected profit and cost yields. Given the current mode, this model allows for either a switch to the other mode or termination of the project, and this happens for both sides of the balance sheet. A novelty in this model is that the related obstacles are nonlinear in the underlying yields, whereas, they are linear in the standard optimal switching problem. The optimal switching problem is formulated in terms of a system of Snell envelopes for the profit and cost yields which act as obstacles to each other. We prove the existence of a continuous minimal solution of this system using an approximation scheme and fully characterize the optimal switching strategy.

Keywords::

• real options
• backward SDEs
• Snell envelope
• stopping time
• optimal switching
• impulse control
• balance sheet
• merger and acquisition

AMS Subject Classification::

• 60G40
• 93E20
• 62P20
• 91B99

Acknowledgements

The financial support from The Swedish Export Credit Corporation (SEK) is gratefully acknowledged. We would like to thank the anonymous referees for their insightful remarks that helped improve both the content and presentation of the paper.

Notes

^1. Email: [email protected]