A Brownian optimal switching problem under incomplete information

TL;DR

This paper investigates an optimal switching problem under incomplete information where a manager makes decisions based on noisy observations of a Brownian motion, and demonstrates how the problem reduces to a full information case using stochastic filtering.

Contribution

It introduces a method to convert an incomplete information switching problem into a full information problem via linear stochastic filtering, and analyzes the value function's behavior with respect to information quality.

Findings

Value function is non-decreasing with more information.

Value function converges to the full information case as noise decreases.

The approach links filtering theory with optimal switching under uncertainty.

Abstract

In this paper we study an incomplete information optimal switching problem in which the manager only has access to noisy observations of the underlying Brownian motion $\{W_t\}_{t \geq 0}$. The manager can, at a fixed cost, switch between having the production facility open or closed and must find the optimal management strategy using only the noisy observations. Using the theory of linear stochastic filtering, we reduce the incomplete information problem to a full information problem, show that the value function is non-decreasing with the amount of information available, and that the value function of the incomplete information problem converges to the value function of the corresponding full information problem as the noise in the observed process tends to $0$.