Optimal Investment Decision Under Switching regimes of Subsidy Support

TL;DR

This paper studies optimal investment decisions under subsidy regimes modeled as switching diffusions, providing a characterization of the value function and optimal strategies using viscosity solutions and convex analysis.

Contribution

It introduces a novel approach to solving infinite-horizon optimal stopping problems with switching regimes, including a unique viscosity solution framework and convexity properties for specific cases.

Findings

Value function characterized as unique viscosity solution.

In homogeneous Markov chain case, value function is the difference of two convex functions.

Provides a systematic method for optimal stopping under subsidy switching regimes.

Abstract

We address the problem of making a managerial decision when the investment project is subsidized, which results in the resolution of an infinite-horizon optimal stopping problem of a switching diffusion driven by either an homogeneous or an inhomogeneous continuous-time Markov chain. We provide a characterization of the value function (and optimal strategy) of the optimal stopping problem. On the one hand, broadly, we can prove that the value function is the unique viscosity solution to a system of HJB equations. On the other hand, when the Markov chain is homogeneous and the switching diffusion is one-dimensional, we obtain stronger results: the value function is the difference between two convex functions.