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In this paper, we present an overview of the recent developments offunctional quantization of stochastic processes, with an emphasis on thequadratic case. Functional quantization is a way to approximate a process,viewed as a Hilbert-valued random variable, using a nearest neighbourprojection on a finite codebook. A special emphasis is made on thecomputational aspects and the numerical applications, in particular the pricingof some path-dependent European options.

Quadratic optimal functional quantization of stochastic processes and numerical applications