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

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  • Matteo Basei

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.

Suggested Citation

  • Matteo Basei, 2018. "Optimal price management in retail energy markets: an impulse control problem with asymptotic estimates," Papers 1803.08166, arXiv.org, revised Mar 2019.
    • Handle: RePEc:arx:papers:1803.08166
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    References listed on IDEAS

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    1. Abel Cadenillas & Tahir Choulli & Michael Taksar & Lei Zhang, 2006. "Classical And Impulse Stochastic Control For The Optimization Of The Dividend And Risk Policies Of An Insurance Firm," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 181-202, January.
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    8. Monique Jeanblanc‐Picqué, 1993. "Impulse Control Method and Exchange Rate," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 161-177, April.
    9. Daniel Mitchell & Haolin Feng & Kumar Muthuraman, 2014. "Impulse Control of Interest Rates," Operations Research, INFORMS, vol. 62(3), pages 602-615, June.
    10. Cadenillas, Abel & Zapatero, Fernando, 1999. "Optimal Central Bank Intervention in the Foreign Exchange Market," Journal of Economic Theory, Elsevier, vol. 87(1), pages 218-242, July.
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    Cited by:

    1. Mike Ludkovski, 2022. "Regression Monte Carlo for Impulse Control," Papers 2203.06539, arXiv.org.
    2. Sadana, Utsav & Reddy, Puduru Viswanadha & Zaccour, Georges, 2021. "Nash equilibria in nonzero-sum differential games with impulse control," European Journal of Operational Research, Elsevier, vol. 295(2), pages 792-805.
    3. Ren'e Aid & Lamia Ben Ajmia & M'hamed Gaigi & Mohamed Mnif, 2021. "Nonzero-sum stochastic impulse games with an application in competitive retail energy markets," Papers 2112.10213, arXiv.org.
    4. Diego Zabaljauregui, 2019. "A fixed-point policy-iteration-type algorithm for symmetric nonzero-sum stochastic impulse control games," Papers 1909.03574, arXiv.org, revised Jun 2020.
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    6. Diego Zabaljauregui, 2020. "Optimal market making under partial information and numerical methods for impulse control games with applications," Papers 2009.06521, arXiv.org.

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