Volatility uncertainty quantification in a stochastic control problem applied to energy

Francisco Bernal, Emmanuel Gobet () and Jacques Printems
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Francisco Bernal: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Emmanuel Gobet: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Jacques Printems: LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées - UPEM - Université Paris-Est Marne-la-Vallée - BEZOUT - Fédération de Recherche Bézout - CNRS - Centre National de la Recherche Scientifique - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12 - CNRS - Centre National de la Recherche Scientifique

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Abstract: This work designs a methodology to quantify the uncertainty of a volatility parameter in a stochastic control problem arising in energy management. The difficulty lies in the non-linearity of the underlying scalar Hamilton-Jacobi-Bellman equation. We proceed by decomposing the unknown solution on a Hermite polynomial basis (of the unknown volatility), whose different coefficients are solution to a system of non-linear PDEs of the same kind. Numerical tests show that computing the first basis elements may be enough to get an accurate approximation with respect to the uncertain volatility parameter. We experiment the methodology in the context of swing contract (energy contract with flexibility in purchasing energy power), this allows to introduce the concept of Uncertainty Value Adjustment (UVA), whose aim is to value the risk of misspecification of the volatility model.

Keywords: chaos expansion; uncertainty quantification; stochastic control; stochastic programming; Swing options; Monte Carlo simulations (search for similar items in EconPapers)
Date: 2019-01-24
Note: View the original document on HAL open archive server: https://hal.science/hal-01784095v1
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Published in Methodology and Computing in Applied Probability, 2019, 22 (1), pp.135-159. ⟨10.1007/s11009-019-09692-x⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01784095

DOI: 10.1007/s11009-019-09692-x

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