A class of Solvable Multiple Entry Problems with Forced Exits

TL;DR

This paper provides a closed-form solution for a complex optimal investment problem involving multiple entries, forced exits, and catastrophe risks, with explicit examples illustrating the theoretical findings.

Contribution

It introduces a solvable model for multiple entry investment problems with forced exits and catastrophe risks, extending previous models with explicit solutions.

Findings

Optimal investment threshold is independent of Bernoulli trial success probability.

Closed-form solutions are derived for general diffusion dynamics and payoff functions.

Explicit examples demonstrate the applicability of the theoretical results.

Abstract

We study an optimal investment problem with multiple entries and forced exits. A closed form solution of the optimisation problem is presented for general underlying diffusion dynamics and a general running payoff function in the case when forced exits occur on the jump times of a Poisson process. Furthermore, we allow the investment opportunity to be subject to the risk of a catastrophe that can occur at the jumps of the Poisson process. More precisely, we attach IID Bernoulli trials to the jump times and if the trial fails, no further re-entries are allowed. We show in the general case that the optimal investment threshold is independent of the success probability is the Bernoulli trials. The results are illustrated with explicit examples.