Optimal extraction with an impact on diffusion-jump pricing

TL;DR

This paper investigates an optimal extraction strategy in a market where the agent's actions negatively impact prices, considering complex price dynamics with jumps and drift, to maximize expected profits.

Contribution

It introduces a model combining impact effects with jump-diffusion price dynamics to determine optimal extraction strategies.

Findings

Derived explicit optimal extraction policies.

Analyzed the impact of jumps on profit maximization.

Provided insights into market impact effects.

Abstract

We study an optimal extraction problem where the agent's actions in the spot market exert an additive proportional negative impact on the commodity price. The commodity price dynamics, prior to any activity by the agent, are evolved by a drifted Brownian motion with jumps. The agent's primary aim is to identify an optimal extraction strategy that maximizes their expected net profits.