Optimal Starting-Stopping and Switching of a CIR Process with Fixed Costs

TL;DR

This paper investigates optimal strategies for starting, stopping, and switching a CIR process with fixed costs, establishing threshold-based solutions and analyzing their dependence on parameters through analytical and numerical methods.

Contribution

It provides a rigorous analysis of threshold-type strategies for the CIR process with fixed costs and links starting-stopping and switching problems under certain conditions.

Findings

Optimal strategies are of threshold type.

Analytical expressions involve confluent hypergeometric functions.

Numerical examples illustrate parameter influence on strategies.

Abstract

This paper analyzes the problem of starting and stopping a Cox-Ingersoll-Ross (CIR) process with fixed costs. In addition, we also study a related optimal switching problem that involves an infinite sequence of starts and stops. We establish the conditions under which the starting-stopping and switching problems admit the same optimal starting and/or stopping strategies. We rigorously prove that the optimal starting and stopping strategies are of threshold type, and give the analytical expressions for the value functions in terms of confluent hypergeometric functions. Numerical examples are provided to illustrate the dependence of timing strategies on model parameters and transaction costs.