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Showing 1 to 10 of 10 for “"Backward stochastic differential equations"”.
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Backward stochastic differential equations with jumps are stable
A backward stochastic differential equation is a stochastic differential equation whose terminal value is known, in contrast to a (forward) stochastic differential equation whose initial value is known, and whose solution has to be adapted to a given filtration. The main aim of this thesis is to …
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Enlargement of Filtration, Backward Stochastic Differential Equations and Optimal Stopping Problems
… application of the enlargement of filtration to backward stochastic differential equations (BSDEs) and optimal stopping problems. In particular, the thesis develops the theory of the progressive enlargement of filtration with multiple random times and their associated marks. Several extensions of …
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SDEs and MFGs towards Machine Learning applications
… domains. Initially, our analysis is centred on Backward Stochastic Differential Equations (BSDEs) featuring time-delayed generators. Subsequently, we direct our interest towards Mean Field Games (MFGs) incorporating absorption aspects, with a focus on the corresponding Master Equation within a …
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Numerical approximations of coupled forward-backward SPDEs with applications
… the numerical approximations of coupled forward-backward stochastic partial differential equations (FBSPDEs) with homogeneous Dirichlet boundary conditions. For the FBSPDE, the finite element method in the spatial domain leads to approximations by finite-dimensional forward-backward stochastic …
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Implementation of numerical Fourier method for second order Taylor schemes
… (1973). It was also in 1973 that the theory of backward stochastic differential equations (BSDEs) was developed by Bismut, Jean-Michel (1973), but it was much later in the literature that BSDEs developed links to contingent claim pricing. This dissertation is a thorough exposition of the survey …
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Mathematical Models For Swing Options And Subprime Mortgage Derivatives.
… methodology using the theory of reflected backward stochastic differential equations and the theory of Snell envelopes. Once the model is constructed, one can use numerical techniques to solve the pricing problem and compute a replicating strategy using forward contracts. The recent burst …
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Feynman-Kac Numerical Techniques for Stochastic Optimal Control
… numerical methods in the solution of forward-backward stochastic differential equations (FBSDEs) appearing in the Feynman-Kac representation of the value function in stochastic optimal control (SOC) problems. First, we propose a novel characterization of FBSDE estimators as either on-policy or …
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Dynamic hedging in illiquid financial markets
… Mathematically, this amounts to study various stochastic optimal control problems with suitable nonlinear dynamics. We introduce a price impact model which accounts for finite market depth, market tightness and finite resilience whose coupled bid- and ask-price dynamics induce convex liquidity …
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Duality for nonlinear filtering
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms