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Study of numerical methods for some stochastic differential equations in finance and modeling of capital distribution in financial market

Abstract : In this thesis, we make some contributions to the modeling of the financial market in the context of stochastic portfolio theory, as well as to the study of numerical methods for some stochastic differential equations in financial modeling and game theory. The market is mod-eled by relative weights of assets and we study a probabilistic scheme for marginal laws of solutions of McKean-Vlasov SDEs. We also develop a probabilistic representation and inte-gration by parts formulae for some stochastic volatility models to obtain unbiased Monte-Carlo estimators of price and sensitivities. Finally we present two algorithms for numerical resolution of FBSDEs arising from mean-field games
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Houzhi Li. Study of numerical methods for some stochastic differential equations in finance and modeling of capital distribution in financial market. General Mathematics [math.GM]. Université Paris Cité, 2021. English. ⟨NNT : 2021UNIP7031⟩. ⟨tel-03550527⟩

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