Functional quantization for pricing derivatives

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HAL Id: inria-00070611

https://hal.inria.fr/inria-00070611

Submitted on 19 May 2006

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Functional quantization for pricing derivatives

Gilles Pagès, Jacques Printems

To cite this version:

Gilles Pagès, Jacques Printems. Functional quantization for pricing derivatives. [Research Report]

RR-5392, INRIA. 2004, pp.53. �inria-00070611�

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ISRN INRIA/RR--5392--FR+ENG

a p p o r t

d e r e c h e r c h e

Thème NUM

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Functional quantization for pricing derivatives.

Gilles Pagès and Jacques Printems

N° 5392

Novembre 2004

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(10)

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(11)

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3Jm 95

(12)

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E(X) =E(Xb^x)

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E(|X−Xb^x|²H |Xb^x) = Xb^x) +|Xb^x|²H

E(|X|²H |Xb^x)− |Xb^x|²H

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kX−Xb^xk²2 = E(|X|²_H)−E(|Xb^x|²_H) =E(|X|²_H)− X

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