Quadratic optimal functional quantization of stochastic processes and numerical applications

Gilles Pagès (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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

Mots clés: functional quantization; optimal quantization; path-dependent option pricing; Quasi-Monte Carlo method; Karhunen-Loève expansion; Romberg extrapolation

Domaines: Probabilités [math.PR]

Gilles Pagès. Quadratic optimal functional quantization of stochastic processes and numerical applications. Quadratic optimal functional quantization of stochastic processes and numerical applications, Aug 2006, Ulm, Germany. pp.101-142, ⟨10.1007/978-3-540-74496-2_6⟩. ⟨hal-00158846⟩