A Class of Solvable Optimal Stopping Problems of Spectrally Negative Jump Diffusions

TL;DR

This paper analyzes a class of spectrally negative jump diffusion optimal stopping problems, providing conditions for explicit solutions, linking them to continuous diffusions, and examining how volatility and jump intensity influence stopping strategies.

Contribution

It introduces a set of conditions under which the value function can be explicitly characterized via nonlinear programming and connects jump diffusion problems to continuous diffusion stopping problems.

Findings

Increased volatility and jump intensity tend to delay optimal exercise.

The value function can be represented through nonlinear programming under certain conditions.

The connection to continuous diffusions aids in characterizing optimal stopping policies.

Abstract

We consider the optimal stopping of a class of spectrally negative jump diffusions. We state a set of conditions under which the value is shown to have a representation in terms of an ordinary nonlinear programming problem. We establish a connection between the considered problem and a stopping problem of an associated continuous diffusion process and demonstrate how this connection may be applied for characterizing the stopping policy and its value. We also establish a set of typically satisfied conditions under which increased volatility as well as higher jump-intensity decelerates rational exercise by increasing the value and expanding the continuation region.