@article {86,
	title = {CVaR hedging using quantization based stochastic approximation algorithm},
	year = {2010},
	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.},
	keywords = {CVaR, quantization, Robbins-Monro algorithm, stochastic approximation, VaR},
	attachments = {http://quantif.maths-fi.com/sites/default/files/CVaR_hedging.pdf},
	author = {Olivier Bardou and Noufel Frikha and Gilles Pag{\`e}s}
}
