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Optimal extraction with an impact on diffusion-jump pricing

Johanna Garzón, Jhonatan S. Mora Rodríguez, Harold A. Moreno-Franco

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.

Optimal extraction with an impact on diffusion-jump pricing

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.
Paper Structure (16 sections, 12 theorems, 126 equations)

This paper contains 16 sections, 12 theorems, 126 equations.

Table of Contents

  1. Introduction
  2. Formulation of the problem
  3. Preliminary results and HJB equation
  4. Derivation of the HJB equation
  5. Verification Theorem
  6. Optimal extraction strategy and construction of a solution to \ref{['eqHJB']}
  7. Verification of optimality
  8. A related optimal stopping problem
  9. Comparative statics analysis
  10. Conclusions and future work
  11. Appendix
  12. Proof of Lemma \ref{['Exp1']}
  13. Proof of Proposition \ref{['pro1']} and Lemma \ref{['ru']}
  14. Proof of Proposition \ref{['pro1']}
  15. Proof of Lemma \ref{['ru']}
  16. ...and 1 more sections

Key Result

Proposition 3.1

The value function $V$ given by fV satisfies the following properties:

Theorems & Definitions (28)

  • Proposition 3.1
  • proof
  • Lemma 3.2
  • Proposition 3.3: Verification theorem
  • proof
  • Proposition 4.1
  • Remark 4.2
  • proof : Proof of Theorem \ref{['teo1']}. First part
  • Lemma 5.1
  • proof : Proof of Theorem \ref{['teo1']}. Second part
  • ...and 18 more