# CVaR hedging using quantization based stochastic approximation algorithm

Abstract : In this paper, we investigate a method based on risk minimization to hedge observable but non-tradable source of risk on financial or energy markets. The optimal portfolio strategy is obtained by minimizing dynamically the Conditional Value-at-Risk (CVaR) using three main tools: stochastic approximation algorithm, optimal quantization and variance reduction techniques (importance sampling (IS) and linear control variable (LCV)) as the quantities of interest are naturally related to rare events. As a first step, we investigate the problem of CVaR regression, which corresponds to a static portfolio strategy where the number of units of each tradable assets is fixed at time 0 and remains unchanged till time $T$. We devise a stochastic approximation algorithm and study its a.s. convergence and rate of convergence. Then, we extend to the dynamic case under the assumption that the process modelling the non-tradable source of risk and financial assets prices are Markov. Finally, we illustrate our approach by considering several portfolios in the incomplete energy market.
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Document type :
Preprints, Working Papers, ...
2010
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https://hal.archives-ouvertes.fr/hal-00547776
Contributor : Noufel Frikha <>
Submitted on : Friday, December 17, 2010 - 12:23:34 PM
Last modification on : Monday, May 29, 2017 - 2:22:22 PM
Document(s) archivé(s) le : Thursday, June 30, 2011 - 1:43:14 PM

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CVaR_hedging.pdf
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• HAL Id : hal-00547776, version 1

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Olivier Bardou, Noufel Frikha, Gilles Pagès. CVaR hedging using quantization based stochastic approximation algorithm. 2010. <hal-00547776>

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