Optimal Portfolio in Intraday Electricity Markets Modelled by L\'evy-Ornstein-Uhlenbeck Processes

TL;DR

This paper develops a mathematical model for optimal trading strategies in intraday electricity markets using Levy-Ornstein-Uhlenbeck processes, providing explicit solutions and numerical methods for practical implementation.

Contribution

It introduces a novel approach to model electricity prices with Levy-driven mean reversion and derives explicit solutions for the optimal portfolio problem.

Findings

Explicit solutions for the HJB equation in two cases

Numerical methods for solving the integral equation for strategies

Analysis of two approximation methods for optimal policies

Abstract

We study an optimal portfolio problem designed for an agent operating in intraday electricity markets. The investor is allowed to trade in a single risky asset modelling the continuously traded power and aims to maximize the expected terminal utility of his wealth. We assume a mean-reverting additive process to drive the power prices. In the case of logarithmic utility, we reduce the fully non-linear Hamilton-Jacobi-Bellman equation to a linear parabolic integro-differential equation, for which we explicitly exhibit a classical solution in two cases of modelling interest. The optimal strategy is given implicitly as the solution of an integral equation, which is possible to solve numerically as well as to describe analytically. An analysis of two different approximations for the optimal policy is provided. Finally, we perform a numerical test by adapting the parameters of a popular electricity spot price model.