Probabilistic methods for semilinear partial differential equations. Applications to finance
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Publication:4933356
DOI10.1051/m2an/2010054zbMath1210.65011OpenAlexW2075910419MaRDI QIDQ4933356
Konstantinos Manolarakis, Dan Crisan
Publication date: 12 October 2010
Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/44674
Nonparametric regression and quantile regression (62G08) Numerical methods (including Monte Carlo methods) (91G60) Monte Carlo methods (65C05) Stochastic calculus of variations and the Malliavin calculus (60H07) Numerical solutions to stochastic differential and integral equations (65C30)
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Cites Work
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- Adapted solution of a backward stochastic differential equation
- Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula
- Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations
- Error expansion for the discretization of backward stochastic differential equations
- On the Monte Carlo simulation of BSDEs: an improvement on the Malliavin weights
- Bounded solutions to backward SDEs with jumps for utility optimization and indifference hedging
- Forward-backward stochastic differential equations and quasilinear parabolic PDEs
- Hedging contingent claims with constrained portfolios
- Reflected solutions of backward SDE's, and related obstacle problems for PDE's
- Backward stochastic differential equations with continuous coefficient
- Convex measures of risk and trading constraints
- A quantization algorithm for solving multidimensional discrete-time optimal stopping problems
- A numerical scheme for BSDEs
- Representation theorems for backward stochastic differential equations
- Backward stochastic differential equations and partial differential equations with quadratic growth.
- On the Malliavin approach to Monte Carlo approximation of conditional expectations
- BSDE with quadratic growth and unbounded terminal value
- Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations
- Representations and regularities for solutions to BSDEs with reflections
- Risk measures via \(g\)-expectations
- A regression-based Monte Carlo method to solve backward stochastic differential equations
- Error analysis of the optimal quantization algorithm for obstacle problems.
- Cubature on Wiener space
- ARBITRAGE IN SECURITIES MARKETS WITH SHORT-SALES CONSTRAINTS
- The Malliavin Calculus and Related Topics
- Multidimensional Stochastic Processes as Rough Paths
- Second-order backward stochastic differential equations and fully nonlinear parabolic PDEs
- Stochastic Differential Utility
- Necessary Conditions for Optimal Control of Stochastic Systems with Random Jumps
- Backward Stochastic Differential Equations in Finance
- Dynamic Programming and Pricing of Contingent Claims in an Incomplete Market
- System Control and Rough Paths
- Solving Backward Stochastic Differential Equations Using the Cubature Method: Application to Nonlinear Pricing
- Space-Time Approach to Non-Relativistic Quantum Mechanics
- Valuing American Options by Simulation: A Simple Least-Squares Approach
- On Distributions of Certain Wiener Functionals
