A Full Balance Sheet Two-modes Optimal Switching problem

TL;DR

This paper introduces a novel finite horizon optimal switching model for full balance sheets, incorporating nonlinear obstacles in profit and cost yields, and characterizes the optimal strategy using a system of interconnected Snell envelopes.

Contribution

It develops a new model with nonlinear obstacles in the optimal switching framework and provides a complete characterization of the optimal strategy.

Findings

Existence of a continuous minimal solution is proven.

The model handles nonlinear obstacles unlike standard linear models.

Optimal switching strategies are fully characterized.

Abstract

We formulate and solve a finite horizon full balance sheet two-modes 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 existence of a continuous minimal solution of this system using an approximation scheme and fully characterize the optimal switching strategy.