Asset pricing with heterogeneous beliefs and illiquidity. Lp (p > 1) Solutions of BSDEs with Generators Satisfying Some Non-uniform Conditions in t and ω. Deep xVA Solver – A Neural Network Based Counterparty Credit Risk Management Framework. Knowledge-based, broadly deployed natural language. The risk-sensitive maximum principle for controlled forward–backward stochastic differential equations. International Journal of Theoretical and Applied Finance. Stochastic differential equations are used in finance (interest rate, stock prices, …), biology (population, epidemics, …), physics (particles in fluids, thermal noise, …), and control and signal processing (controller, filtering, …). Central infrastructure for Wolfram's cloud products & services. Backward Stochastic Differential Equations Driven by G-Brownian Motion with Double Reflections. A Regime-Switching Model with Applications to Finance: Markovian and Non-Markovian Cases. A BSDE-based approach for the optimal reinsurance problem under partial information. A Monte Carlo method for backward stochastic differential equations with Hermite martingales. Number of times cited according to CrossRef: A Multistep Scheme to Solve Backward Stochastic Differential Equations for Option Pricing on GPUs. There are several applications of first-order stochastic differential equations to finance. On the partial controllability of SDEs and the exact controllability of FBSDES. WienerProcess — Wiener process or Brownian motion, OrnsteinUhlenbeckProcess — Ornstein–Uhlenbeck process, BrownianBridgeProcess  ▪  GeometricBrownianMotionProcess  ▪  CoxIngersollRossProcess, StratonovichProcess — Stratonovich sde process, RandomFunction — simulate an sde process (Euler–Muryama, stochastic Runge–Kutta, …), SliceDistribution — distribution of states at particular times, CovarianceFunction  ▪  CorrelationFunction  ▪  AbsoluteCorrelationFunction, Enable JavaScript to interact with content and submit forms on Wolfram websites. Journal of Computational and Applied Mathematics. Stochastic Modelling in Asset Prices The Black–Scholes World Irregular barrier reflected BDSDEs with general jumps under stochastic Lipschitz and linear growth conditions. Linear–quadratic optimal control for time-delay stochastic system with recursive utility under full and partial information. Gaussian density estimates for solutions of fully coupled forward‐backward SDEs. Reflected BSDES with stochastic Monotone Generator and Application to Valuing American Options. Japan Journal of Industrial and Applied Mathematics. Backward Stochastic Differential Equations Driven by G-Brownian Motion with Uniformly Continuous Coefficients in (y, z). Anticipated backward stochastic differential equations with quadratic growth. A framework of BSDEs with stochastic Lipschitz coefficients. Learn more. Please check your email for instructions on resetting your password. The Wolfram Language provides common special sdes specified by a few parameters as well as general Ito and Stratonovich sdes and systems specified by their differential equations. A Study on a New Class of Backward Stochastic Differential Equation. Enhancing risk stratification for life‐threatening ventricular arrhythmias in dilated cardiomyopathy: the peril and promise of precision medicine. Particles Systems for mean reflected BSDEs. 1. Communications in Statistics - Theory and Methods. Mean square rate of convergence for random walk approximation of forward-backward SDEs. The full text of this article hosted at is unavailable due to technical difficulties. Backward stochastic Volterra integral equations — Representation of adapted solutions. Gauss-Wiener processes have been used to model variables ranging from those governing economic production to the rate of inflation and to interest rates. Continuous Viscosity Solutions to Linear-Quadratic Stochastic Control Problems with Singular Terminal State Constraint. Time-consistent investment-proportional reinsurance strategy with random coefficients for mean–variance insurers. Dynamic risk measures for processes via backward stochastic differential equations. Nonparametric drift estimation for diffusions with jumps driven by a Hawkes process. A global maximum principle for optimal control of general mean-field forward-backward stochastic systems with jumps. These equations, first introduced by Pardoux and Peng (1990), are useful for the theory of contingent claim valuation, especially cases with constraints and for the theory of recursive utilities, introduced by Duffie and Epstein (1992a, 1992b). Backward stochastic differential equations with unbounded generators. New results on common properties of the products AC and BA, II. Mean-variance asset-liability management with inside information. BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets. L2-regularity of solutions to linear backward stochastic heat equations, and a numerical application. INTRODUCTION Since the pioneering work of Merton there has been phenomenal growth in the use of stochastic differential equations to aid in the analysis of problems in finance. Stochastic Differential Equations in Finance and Monte Carlo Simulations Xuerong Mao Department of Statistics and Modelling Science University of Strathclyde Glasgow, G1 1XH China 2009 Xuerong Mao SM and MC Simulations. Institute of Mathematics, Shandong University, Jinan, China, Equipe de Mathématiques, Université de Marne la Vallée, Noisy–Le–Grand, France. Generalized mean-field backward stochastic differential equations and related partial differential equations. Singular optimal control problems with recursive utilities of mean‐field type. Random Operators and Stochastic Equations. Learn how, Wolfram Natural Language Understanding System. Adding noise to Markov cohort state‐transition model in decision modeling and cost‐effectiveness analysis. Stochastic recursive optimal control problem with obstacle constraint involving diffusion type control. Backward stochastic optimal control with mixed deterministic controller and random controller and its applications in linear-quadratic control. On the well‐posedness of coupled forward–backward stochastic differential equations driven by Teugels martingales. A new numerical method for 1-D backward stochastic differential equations without using conditional expectations. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. A Risk-Sharing Framework of Bilateral Contracts. Revolutionary knowledge-based programming language. Stochastic differential equations (sdes) occur where a system described by differential equations is influenced by random noise. Density Estimates for the Solutions of Backward Stochastic Differential Equations Driven by Gaussian Processes. Systems of Ergodic BSDEs Arising in Regime Switching Forward Performance Processes. Journal of Mathematical Analysis and Applications. The symbolic representation of sde processes allows a uniform way to compute a variety of properties, from simulation and mean and covariance functions to full state distributions at different times. Advection‐diffusion dynamics with nonlinear boundary flux as a model for crystal growth. Learn about our remote access options. BSDEs driven by G-Brownian motion with time-varying Lipschitz condition. Backward stochastic differential equations (BSDEs) are a new class of stochastic differential equations, whose value is prescribed at the terminal time T. BSDEs have received considerable attention in the probability literature in last 20 years because BSDEs provide a probabilistic formula for the solution of certain classes of quasilinear Optimal control for stochastic Volterra equations with multiplicative Lévy noise. Deep neural network framework based on backward stochastic differential equations for pricing and hedging American options in high dimensions. Option valuation and hedging using an asymmetric risk function: asymptotic optimality through fully nonlinear partial differential equations. Maximum Principle for Stochastic Recursive Optimal Control Problem under Model Uncertainty. The preeminent environment for any technical workflows. Space mapping-based receding horizon control for stochastic interacting particle systems: dogs herding sheep.