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Convex Concentration for Some Additive Functionals of Jump Stochastic Differential Equations

Acta Mathematica Sinica,English Series 2013年第8期29卷 1449-1458页

作者： Yutao MA nicolas privault School of Mathematical Sciences and Laboratory for Mathematics and Complex Systems Beijing Normal University School of Physical and Mathematical Sciences Nanyang Technological University

Using forward-backward stochastic calculus, we prove convex concentration inequalities for some additive functionals of the solution of stochastic differential equations with jumps admitting an invariant probability measure. As a consequence, transportation-information inequalities are obtained and bounds on option prices for interest rate derivatives are given as an application.

关键词： Convex concentration inequalities transportation-information inequalities stochastic differential equations with jumps interest rate derivatives

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Stochastic ordering by g-expectations

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Probability, Uncertainty and Quantitative Risk 2021年第1期6卷 61-98页

作者： Sel Ly nicolas privault School of Physical and Mathematical Sciences Division of Mathematical SciencesNanyang Technological UniversitySingapore 637371

We derive sufficient conditions for the convex and monotonic g-stochastic ordering of diffusion processes under nonlinear g-expectations and *** approach relies on comparison results for forward-backward stochastic differential equations and on several extensions of convexity,monotonicity,and continuous dependence properties for the solutions of associated semilinear parabolic partial differential *** to contingent claim price comparison under different hedging portfolio constraints are provided.

关键词： Stochastic ordering g-expectation g-evaluation g-risk measures Forward-backward stochastic differential equations Parabolic PDEs Propagation of convexity

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Numerical Solution of the Incompressible Navier-Stokes Equation by a Deep Branching Algorithm

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Communications in Computational Physics 2023年第7期34卷 261-289页

作者： Jiang Yu Nguwi Guillaume Penent nicolas privault School of Physical and Mathematical Sciences Nanyang Technological UniversitySingapore 637371Singapore

We present an algorithm for the numerical solution of systems of fully nonlinear PDEs using stochastic coded branching *** approach covers functional nonlinearities involving gradient terms of arbitrary orders,and it requires only a boundary condition over space at a given terminal time T instead of Dirichlet or Neumann boundary conditions at all times as in standard *** implementation relies on Monte Carlo estimation,and uses neural networks that perform a meshfree functional estimation on a space-time *** algorithm is applied to the numerical solution of the Navier-Stokes equation and is benchmarked to other implementations in the cases of the Taylor-Green vortex and Arnold-Beltrami-Childress flow.

关键词： Fully nonlinear PDEs systems of PDEs Navier-Stokes equations Monte Carlo method deep neural network branching process random tree

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