Optimal price management in retail energy markets: an impulse control problem with asymptotic estimates

TL;DR

This paper models a retailer's optimal energy pricing strategy as an impulse control problem, deriving analytical solutions, asymptotic behavior, and numerical results to inform pricing decisions in energy markets.

Contribution

It introduces a stochastic impulse control framework for energy pricing, providing analytical existence results and asymptotic estimates related to intervention costs.

Findings

Optimal price intervention strategy characterized

Continuation region measure asymptotic to the fourth root of cost

Numerical results illustrating the model's implications

Abstract

We consider a retailer who buys energy in the wholesale market and resells it to final consumers. The retailer has to decide when to intervene to change the price he asks to his customers, in order to maximize his income. We model the problem as an infinite-horizon stochastic impulse control problem. We characterize an optimal price strategy and provide analytical existence results for the equations involved. We then investigate the dependence on the intervention cost. In particular, we prove that the measure of the continuation region is asymptotic to the fourth root of the cost. Finally, we provide some numerical results and consider a suitable extension of the model.