An Exponential Cox-Ingersoll-Ross Process as Discounting Factor

TL;DR

This paper studies optimal dividend and spending strategies when the discounting factor follows an exponential Cox-Ingersoll-Ross process, providing explicit solutions in deterministic cases and a method for small volatility Brownian cases.

Contribution

It introduces a novel model with an exponential CIR discounting factor and derives explicit and approximate optimal strategies for different surplus processes.

Findings

Explicit optimal strategies in the deterministic case.

A method to show constant-barrier strategies for small volatility.

Insights into the impact of stochastic discounting on optimal policies.

Abstract

We consider an economic agent (a household or an insurance company) modelling its surplus process by a deterministic process or by a Brownian motion with drift. The goal is to maximise the expected discounted spendings/dividend payments, given that the discounting factor is given by an exponential CIR process. In the deterministic case, we are able to find explicit expressions for the optimal strategy and the value function. For the Brownian motion case, we offer a method allowing to show that for a small volatility the optimal strategy is a constant-barrier strategy.