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Robust optimal control for a consumption-investment problem
We give an explicit PDE characterization for the solution of the problem of maximizing the utility of both terminal wealth and intertemporal...
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Existence and Uniqueness of Solutions for two Classes of Functional Equations Arising in Dynamic Programming
In this paper we establish the existence, uniqueness and iterative approximation of solutions for two classes of functional equations arising in...
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PDE Approach to Utility Maximization for Market Models with Hidden Markov Factors
We consider the problem of maximizing expected utility from terminal wealth for a power utility of the risk-averse type assuming that the dynamics of...
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Fractional Hamilton-Jacobi equation for the optimal control of nonrandom fractional dynamics with fractional cost function
By using the variational calculus of fractional order, one derives a Hamilton-Jacobi equation and a Lagrangian variational approach to the optimal...
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The Geometry of the Solution Set of Nonlinear Optimal Control Problems
In an optimal control problem one seeks a time-varying input to a dynamical systems in order to stabilize a given target trajectory, such that a...
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Local Fields of Extremals for Optimal Control Problems with State Constraints of Relative Degree 1
A local embedding of a boundary arc into a field of extremals is constructed for single-input optimal control problems with state space constraints...
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Properties of Solutions for Certain Functional Equations Arising in Dynamic Programming
In this paper, we introduce and study properties of solutions for the following functional equation arising in dynamic programming of multistage...
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Remarks on Risk-Sensitive Control Problems
The main purpose of this paper is to investigate the asymptotic behavior of the discounted risk-sensitive control problem for periodic diffusion...
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Differential Games of inf-sup Type and Isaacs Equations
Motivated by the work of Fleming, we provide a general framework to associate inf-sup type values with the Isaacs equations. We show that upper and...
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Error estimation and adaptive discretization for the discrete stochastic Hamilton–Jacobi–Bellman equation
Generalizing an idea from deterministic optimal control, we construct a posteriori error estimates for the spatial discretization error of the...
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Piecewise Deterministic Markov Control Processes with Feedback Controls and Unbounded Costs
The control of piecewise-deterministic processes is studied where only local boundedness of the data is assumed. Moreover the discount rate may be...
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Viscosity Solutions of HJB Equations with Unbounded Data and Characteristic Points
We study a class of infinite horizon and exit-time control problems for nonlinear systems with unbounded data using the dynamic programming...
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Optimal Control of Hybrid Systems with an Infinite Set of Discrete States
Hybrid control systems are described by a family of continuous subsystems and a set of logic rules for switching between them. This paper concerns a...
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Financial Risk Modelling and Econometric Inference
In finance, the explicit modelling of uncertainty takes on a particularly important role. The values of financial derivatives increase in the return...
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The Problem of Super-replication under Constraints
These notes present an overview of the problem of super-replication under portfolio constraints. We start by examining the duality approach and its...
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Optimal investment for investors with state dependent income, and for insurers
Abstract. An optimal control problem is considered where a risky asset is used for investment, and this investment is financed by initial wealth as...
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A Linear PDE Approach to the Bellman Equation of Ergodic Control with Periodic Structure
Abstract. In this paper we give a new proof of the existence result of Bensoussan [1, Theorem II-6.1] for the Bellman equation of ergodic control...
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Robust Optimal Stop**-Time Control for Nonlinear Systems
Abstract. We formulate a robust optimal stop**-time problem for a state-space system and give the connection between various notions of lower value...
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Dynamic programming for stochastic target problems and geometric flows
Given a controlled stochastic process, the reachability set is the collection of all initial data from which the state process can be driven into a...
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Dynamic programming for some optimal control problems with hysteresis
We study an infinite horizon optimal control problem for a system with two state variables. One of them has the evolution governed by a controlled...