Numerical methods and models in market risk and financial valuations Area
type: Dataset
description: Numerical methods and models in market risk and financial valuations area This work is organized in two themes : (i) A novel numerical method to price options on many assets, (ii) The liquidity risk, the limit order book modeling and the market microstructure. First theme : Greedy algorithms and applications for solving partial differential equations in high dimension Many problems of interest for various applications (material sciences, finance, etc) involve high- dimensional partial differential equations (PDEs). The typical example in finance is the pricing of a basket option, which can be obtained by solving the Black-Scholes PDE with dimension the number of underlying assets. We propose to investigate an algorithm which has been recently proposed and ana- lyzed in [ACKM06, BLM09] to solve such problems and try to circumvent the curse of dimensionality. The idea is to represent the solution as a sum of tensor products and to compute iteratively the terms of this sum using a greedy algorithm. The resolution of high dimensional partial differential equations is highly related to the representation of high dimensional functions. In Chapter 1, we describe various linear approaches existing in literature to represent high dimensional functions and we introduce the high dimensional problems in finance that we will address in this work. The method studied in this manuscript is a non-linear approximation method called the Proper Generalized Decomposition. Chapter 2 shows the application of this method to approximate the so- lution of a linear PDE (the Poisson problem) and also to approximate a square integrable function by a sum of tensor products. A numerical study of this last problem is presented in Chapter 3. The Poisson problem and the approximation of a square integrable function will serve as basis in Chapter 4 for solving the Black-Scholes equation using the PGD approach. In numerical experiments, we obtain results for up to 10 underlyings. Besides the approxima…
landing page: https://theses.hal.science/tel-00937131
keyword: equations-aux-derivees-partielles
keyword: infoeu-reposemanticsdoctoralthesis
keyword: markets-microstructure
keyword: mathmath-apmathematics-mathanalysis-of-pdes-mathap
keyword: mathmath-ocmathematics-mathoptimization-and-control-mathoc
keyword: microstructure-des-marches
keyword: optimisation-et-controle
keyword: optimization-and-control
keyword: partial-differential-equations
keyword: pricing
keyword: qfinprquantitative-finance-q-finpricing-of-securities-q-finpr
keyword: qfintrquantitative-finance-q-fintrading-and-market-microstructure-q-fintr
keyword: theses
issued: 2026-05-07T05:53:02.268109
modified: 2026-05-07T05:53:02.268113
language: en
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Numerical methods and models in market risk and financial valuations Area
type: Distribution
format: HTML
access URL: https://theses.hal.science/tel-00937131
issued: 2026-05-07T05:53:02.275660
modified: 2026-05-07T05:53:02.253363