# Learning from the past in an irreversible investment problem

## TL;DR

This paper models an irreversible investment problem where learning from past information influences the timing of investments, using a recursive stopping problem approach with explicit boundaries.

## Contribution

It introduces a novel recursive framework for investment decisions involving learning from past information, with semi-explicit solutions for optimal stopping boundaries.

## Key findings

- Existence of one-sided stopping boundaries at each recursion step
- Optimal investment strategy characterized by a sequence of semi-explicit boundaries
- Numerical solutions and comparative statistics validate the approach

## Abstract

We consider an irreversible investment problem under incomplete information, where the investor decides whether and when to make investments in a project. Upon investment, the investor acquires previously hidden information from the project's past (''learning from the past''), and so the learning rate of the problem is controlled by investing. We set up this original problem as an recursively defined stopping problem, where the learning rate is accelerated after each recursion step. To solve the problem, we show that at each step, there indeed exists a one-sided stopping boundary under general conditions. We proceed to present the optimal investment strategy as a sequence of semi-explicit stopping boundaries derived from smooth fit conditions. Feasibility of our approach is then demonstrated by solving boundaries numerically and by illustrating comparative statistics.