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On the Nonlinear Factorization Equation in a Normed Ring
AbstractA general form of nonlinear factorization equations in rings and normed rings is considered. Using nonlinear factorization equation, two...
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The Cauchy Problem for a Stochastic Parabolic Equation with an Argument Deviation
The Cauchy problem for a stochastic nonlinear equation of parabolic type with delay is considered. Using Green’s function, a formula is derived for...
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Artificial Viscosity Joint Spacetime Multigrid Method for Hamilton–Jacobi–Bellman and Kolmogorov–Fokker–Planck System Arising from Mean Field Games
In this paper, we study numerical solutions for the Hamilton-Jacobi-Bellman (HJB) and Kolmogorov–Fokker–Planck (KFP) equations arising from mean...
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The Problem of Determining the Coefficient Multiplying a Power-Law Gradient Nonlinearity in a Semilinear Wave Equation
AbstractWe consider a one-dimensional inverse problem of determining the coefficient multiplying a power-law gradient nonlinearity in a semilinear...
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Representation of Weak Solutions of Convex Hamilton–Jacobi–Bellman Equations on Infinite Horizon
In the present paper, it is provided a representation result for the weak solutions of a class of evolutionary Hamilton–Jacobi–Bellman equations on...
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Solving high-dimensional Hamilton–Jacobi–Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space
Optimal control of diffusion processes is intimately connected to the problem of solving certain Hamilton–Jacobi–Bellman equations. Building on...
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Numerical methods for an algebraic Riccati equation arising in transport theory in the critical case
In this paper, we are interested in computing the minimal positive solution of an algebraic Riccati equation arising in transport theory. The...
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A BSDE Approach to Stochastic Differential Games Involving Impulse Controls and HJBI Equation
This paper focuses on zero-sum stochastic differential games in the framework of forward-backward stochastic differential equations on a finite time...
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On Locally Concave Functions on Simplest Nonconvex Domains
We prove that certain Bellman functions of several variables are the minimal locally concave functions. This generalizes earlier results about...
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Maximum principles and the method of moving planes for the uniformly elliptic nonlocal Bellman operator and applications
In this paper, we establish various maximum principles and develop the method of moving planes for equations involving the uniformly elliptic...
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Dissipativity in Infinite Horizon Optimal Control and Dynamic Programming
In this paper we extend dynamic programming techniques to the study of discrete-time infinite horizon optimal control problems on compact control...
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Guaranteed Deterministic Approach to Superhedging: Sensitivity of Solutions of the Bellman-Isaacs Equations and Numerical Methods
We consider a guaranteed deterministic formulation for the super-replication problem in discrete time: find a guaranteed coverage of a contingent...
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Monotone and Second Order Consistent Scheme for the Two Dimensional Pucci Equation
We introduce a new strategy for the design of second-order accurate discretizations of non-linear second order operators of Bellman type, which...
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Unifying incidence and prevalence under a time-varying general branching process
Renewal equations are a popular approach used in modelling the number of new infections, i.e., incidence, in an outbreak. We develop a stochastic...
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Determination of a Coefficient and Kernel in a Two-dimensional Fractional Integrodifferential Equation
AbstractThis paper is devoted to obtaining a unique solution to an inverse problem for a two-dimensional time-fractional integrodifferential...
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A novel outlook to the an alternative equation for modelling shallow water wave: Regularised Long Wave (RLW) equation
In the present study, numerical solutions of the regularized long-wave (RLW) equation which is commonly taken as an alternative equation for...
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The Parametrically Extended Kardar–Parisi–Zhang Equation, Its Dark-Type Generalization, and Integrability
A physical problem of existence of conservation laws for a parametrically dependent Kardar–Parisi–Zhang equation, describing a spin glass growth...
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A parameter-uniform numerical method for singularly perturbed Burgers’ equation
In this article, we propose a parameter-uniformly convergent numerical method for singularly perturbed Burgers’ initial-boundary value problem....
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Optimal Portfolio Strategies
In this chapter, we consider optimization approaches in investment decisions, both in the discrete time and the continuous time setup, making use of...