Mathematical Methods in the Applied Sciences. Instant deployment across cloud, desktop, mobile, and more. Two-player zero-sum stochastic differential games with regime switching. L2-regularity of solutions to linear backward stochastic heat equations, and a numerical application. Advection‐diffusion dynamics with nonlinear boundary flux as a model for crystal growth. The preeminent environment for any technical workflows. Time-consistent investment-proportional reinsurance strategy with random coefficients for mean–variance insurers. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Japan Journal of Industrial and Applied Mathematics. Anticipated backward stochastic differential equations with quadratic growth. A framework of BSDEs with stochastic Lipschitz coefficients. Linear–quadratic optimal control for time-delay stochastic system with recursive utility under full and partial information. Lecture 21: Stochastic Differential Equations In this lecture, we study stochastic di erential equations. Option valuation and hedging using an asymmetric risk function: asymptotic optimality through fully nonlinear partial differential equations. Backward Stochastic Differential Equations Driven by G-Brownian Motion with Uniformly Continuous Coefficients in (y, z). Gain/Loss Asymmetric Stochastic Differential Utility. 1. Laboratoire de Probabilités, CNRS–URA 224, Université de Paris VI, Paris, France. Rupture Dynamics of the 2012 Nicoya M 7.6 Earthquake: Evidence for Low Strength on the Megathrust. Indifference pricing of pure endowments via BSDEs under partial information. Anticipated backward doubly SDEs with generators in stochastic Lipschitz condition. Backward Stochastic Differential Equations Driven by G-Brownian Motion with Double Reflections. 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. The risk-sensitive maximum principle for controlled forward–backward stochastic differential equations. -expectations in general filtration spaces Besov regularity for solutions of elliptic equations with variable exponents. New results on common properties of the products AC and BA, II. Asset pricing with heterogeneous beliefs and illiquidity. Adding noise to Markov cohort state‐transition model in decision modeling and cost‐effectiveness analysis. Jensen’s inequality for Duality-based a posteriori error estimates for some approximation schemes for optimal investment problems. Modern Stochastics: Theory and Applications. See Chapter 9 of [3] for a thorough treatment of the materials in this section. Lp solution of general mean-field BSDEs with continuous coefficients. Curated computable knowledge powering Wolfram|Alpha. Enhancing risk stratification for life‐threatening ventricular arrhythmias in dilated cardiomyopathy: the peril and promise of precision medicine. Uncertainty and filtering of hidden Markov models in discrete time. On the dynamic representation of some time-inconsistent risk measures in a Brownian filtration. Revolutionary knowledge-based programming language. BSDEs driven by cylindrical martingales with application to approximate hedging in bond markets. A BSDE-based approach for the optimal reinsurance problem under partial information. Stochastic Processes and their Applications. Gauss-Wiener processes have been used to model variables ranging from those governing economic production to the rate of inflation and to interest rates. We are concerned with different properties of backward stochastic differential equations and their applications to finance. Number of times cited according to CrossRef: A Multistep Scheme to Solve Backward Stochastic Differential Equations for Option Pricing on GPUs. Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping Information. Irregular barrier reflected BDSDEs with general jumps under stochastic Lipschitz and linear growth conditions. 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. Regulation of Renewable Resource Exploitation. The full text of this article hosted at iucr.org is unavailable due to technical difficulties. In financial modelling, SDEs with jumps are often used to describe the dynamics of state variables such as credit ratings, stock indices, interest rates, exchange rates … Extended backward stochastic Volterra integral equations, Quasilinear parabolic equations, and Feynman–Kac formula. Backward stochastic Volterra integral equations — Representation of adapted solutions. 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. Learn how, Wolfram Natural Language Understanding System. Particles Systems for mean reflected BSDEs. Stochastic recursive optimal control problem with obstacle constraint involving diffusion type control. Mean-variance asset–liability management with partial information and uncertain time horizon. Stochastic differential equations We would like to solve di erential equations of the form dX= (t;X(t))dtX+ ˙(t; (t))dB(t) Representation theorems for generators of BSDEs and the extended g-expectations in probability spaces with general filtration. Learn more. Journal of Mathematical Analysis and Applications. Probability, Uncertainty and Quantitative Risk. Communications in Statistics - Theory and Methods. Near-optimal control problems for forward-backward regime-switching systems. Backward stochastic optimal control with mixed deterministic controller and random controller and its applications in linear-quadratic control. . Knowledge-based, broadly deployed natural language. Maximum principle for infinite horizon optimal control of mean-field backward stochastic systems with delay and noisy memory. Use the link below to share a full-text version of this article with your friends and colleagues. 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. Mean square rate of convergence for random walk approximation of forward-backward SDEs. For example, according to the constant volatility approach, it is known that the derivative's underlying asset price follows a standard model for geometric Brownian motion: d X t = μ X t d t + σ X t d W t Discontinuous Nash equilibrium points for nonzero-sum stochastic differential games. Systems of Ergodic BSDEs Arising in Regime Switching Forward Performance Processes. Well-posedness of scalar BSDEs with sub-quadratic generators and related PDEs. Contracting Theory with Competitive Interacting Agents. Forward-backward SDEs with distributional coefficients. Stochastic differential equations (sdes) occur where a system described by differential equations is influenced by random noise.

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