The Annals of Applied Probability, ISSN 1050-5164, 4/2015, Volume 25, Issue 2, pp. 823 - 859

We consider a nondominated model of a discrete-time financial market where stocks are traded dynamically, and options are available for static hedging. In a...

Fundamental Theorem of Asset Pricing | Nondominated model | Optional decomposition | Knightian uncertainty | Martingale measure | Superhedging | martingale measure | PRICES | FUNDAMENTAL THEOREM | optional decomposition | CONTINGENT CLAIMS | STATISTICS & PROBABILITY | superhedging | nondominated model | Probability | Mathematics | 93E20 | 49L20 | 60G42 | 91B28

Fundamental Theorem of Asset Pricing | Nondominated model | Optional decomposition | Knightian uncertainty | Martingale measure | Superhedging | martingale measure | PRICES | FUNDAMENTAL THEOREM | optional decomposition | CONTINGENT CLAIMS | STATISTICS & PROBABILITY | superhedging | nondominated model | Probability | Mathematics | 93E20 | 49L20 | 60G42 | 91B28

Journal Article

The Annals of Applied Probability, ISSN 1050-5164, 2/2014, Volume 24, Issue 1, pp. 312 - 336

We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade...

Call options | Investors | Arbitrage | Transportation | Ordinary differential equations | Financial securities | Mathematics | Stopping distances | Preprints | Martingales | Optimal control | Convex duality | Volatility uncertainty | MAXIMUM | CONTINGENT CLAIMS | STATISTICS & PROBABILITY | volatility uncertainty | OPTIMAL TRANSPORTATION | convex duality | 49L20 | 60J60 | 49L25 | 35K55

Call options | Investors | Arbitrage | Transportation | Ordinary differential equations | Financial securities | Mathematics | Stopping distances | Preprints | Martingales | Optimal control | Convex duality | Volatility uncertainty | MAXIMUM | CONTINGENT CLAIMS | STATISTICS & PROBABILITY | volatility uncertainty | OPTIMAL TRANSPORTATION | convex duality | 49L20 | 60J60 | 49L25 | 35K55

Journal Article

The Annals of Probability, ISSN 0091-1798, 3/2015, Volume 43, Issue 2, pp. 572 - 604

We introduce a new class of backward stochastic differential equations in which the T-terminal value YT of the solution (Y, Z) is not fixed as a random...

Stochastic target | Backward stochastic differential equations | Optimal control | stochastic target | optimal control | STATISTICS & PROBABILITY | STOCHASTIC TARGET PROBLEMS | Probability | Mathematics | 60H10 | 93E20 | 49L20 | 91G80

Stochastic target | Backward stochastic differential equations | Optimal control | stochastic target | optimal control | STATISTICS & PROBABILITY | STOCHASTIC TARGET PROBLEMS | Probability | Mathematics | 60H10 | 93E20 | 49L20 | 91G80

Journal Article

Mathematical Programming, ISSN 0025-5610, 10/2010, Volume 125, Issue 2, pp. 235 - 261

We introduce the concept of a Markov risk measure and we use it to formulate risk-averse control problems for two Markov decision models: a finite horizon...

Theoretical, Mathematical and Computational Physics | Nonsmooth Newton’s method | Secondary 91A25 | Mathematics | Value iteration | Policy iteration | Min-max Markov models | Mathematical Methods in Physics | 90C40 | 93E20 | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Dynamic risk measures | Numerical Analysis | Combinatorics | Markov risk measures | 91B30 | Primary 49L20 | Nonsmooth Newton's method | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CRITERION | STOCHASTIC-DOMINANCE | UTILITY | Markov processes | Convergence (Social sciences) | Management science | Policies | Mathematical analysis | Horizon | Mathematical models | Dynamic programming | Iterative methods | Convergence

Theoretical, Mathematical and Computational Physics | Nonsmooth Newton’s method | Secondary 91A25 | Mathematics | Value iteration | Policy iteration | Min-max Markov models | Mathematical Methods in Physics | 90C40 | 93E20 | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Dynamic risk measures | Numerical Analysis | Combinatorics | Markov risk measures | 91B30 | Primary 49L20 | Nonsmooth Newton's method | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CRITERION | STOCHASTIC-DOMINANCE | UTILITY | Markov processes | Convergence (Social sciences) | Management science | Policies | Mathematical analysis | Horizon | Mathematical models | Dynamic programming | Iterative methods | Convergence

Journal Article

Stochastic Models, ISSN 1532-6349, 10/2019, Volume 35, Issue 4, pp. 469 - 495

In this article, we consider an optimal execution problem with fixed time horizon and bounded transaction rate, which is more natural in practice. We show...

Constrained price impact | 93E20 | 49L20 | stochastic bang-bang control | optimal order execution | 91G80

Constrained price impact | 93E20 | 49L20 | stochastic bang-bang control | optimal order execution | 91G80

Journal Article

The Annals of Applied Probability, ISSN 1050-5164, 6/2014, Volume 24, Issue 3, pp. 899 - 934

We study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which...

Viscosity | Determinism | Mathematical theorems | Differential games | Mathematical functions | Dynamic programming | Gross domestic product | Stopping distances | Martingales | Stochastic game | Geometric dynamic programming principle | Stochastic target | Viscosity solution | VISCOSITY SOLUTIONS | viscosity solution | G-BROWNIAN MOTION | CALCULUS | UNCERTAINTY | DIFFERENTIAL-EQUATIONS | STATISTICS & PROBABILITY | G-EXPECTATION | geometric dynamic programming principle | stochastic game | Probability | Mathematics | 91A23 | 49L20 | 49N70 | 91A60 | 49L25

Viscosity | Determinism | Mathematical theorems | Differential games | Mathematical functions | Dynamic programming | Gross domestic product | Stopping distances | Martingales | Stochastic game | Geometric dynamic programming principle | Stochastic target | Viscosity solution | VISCOSITY SOLUTIONS | viscosity solution | G-BROWNIAN MOTION | CALCULUS | UNCERTAINTY | DIFFERENTIAL-EQUATIONS | STATISTICS & PROBABILITY | G-EXPECTATION | geometric dynamic programming principle | stochastic game | Probability | Mathematics | 91A23 | 49L20 | 49N70 | 91A60 | 49L25

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 6/2019, Volume 79, Issue 3, pp. 1456 - 1476

In Eikonal equations, rarefaction is a common phenomenon known to degrade the rate of convergence of numerical methods. The “factoring” approach alleviates...

Computational Mathematics and Numerical Analysis | 65N12 | Eikonal | Theoretical, Mathematical and Computational Physics | Factoring | Rarefaction fans | Mathematics | 49L20 | Algorithms | Mathematical and Computational Engineering | 49N90 | Robotic navigation | Fast Marching | 49L25 | 65N22 | MATHEMATICS, APPLIED

Computational Mathematics and Numerical Analysis | 65N12 | Eikonal | Theoretical, Mathematical and Computational Physics | Factoring | Rarefaction fans | Mathematics | 49L20 | Algorithms | Mathematical and Computational Engineering | 49N90 | Robotic navigation | Fast Marching | 49L25 | 65N22 | MATHEMATICS, APPLIED

Journal Article

International Journal of Control, ISSN 0020-7179, 10/2019, Volume 92, Issue 10, pp. 2263 - 2273

In this article, optimal control problems of differential equations with delays are investigated for which the associated Hamilton-Jacobi-Bellman (HJB)...

49L20 | optimal control | Hamilton-Jacobi-Bellman equations | differential equations with delays | viscosity solutions | 34K35 | 49L25 | EXISTENCE | INFINITE DIMENSIONS | TIME-TO-BUILD | AUTOMATION & CONTROL SYSTEMS | UNIQUENESS | Viscosity | Nonlinear equations | Equations of state | Partial differential equations | Production planning | Mathematical analysis | Optimal control | Nonlinear differential equations | Control theory

49L20 | optimal control | Hamilton-Jacobi-Bellman equations | differential equations with delays | viscosity solutions | 34K35 | 49L25 | EXISTENCE | INFINITE DIMENSIONS | TIME-TO-BUILD | AUTOMATION & CONTROL SYSTEMS | UNIQUENESS | Viscosity | Nonlinear equations | Equations of state | Partial differential equations | Production planning | Mathematical analysis | Optimal control | Nonlinear differential equations | Control theory

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 5/2016, Volume 169, Issue 2, pp. 671 - 691

We take a new look at the relation between the optimal transport problem and the Schrödinger bridge problem from a stochastic control perspective. Our aim is...

60J60 | Mathematics | Theory of Computation | Optimal transport | 28A50 | Optimization | Schrödinger bridge | 49L20 | 49J20 | Calculus of Variations and Optimal Control; Optimization | 35Q35 | Stochastic control | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | MATHEMATICS, APPLIED | Schrodinger bridge | MECHANICS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FLUID | TERMS | QUANTUM-THEORY | Bridges | Fluid dynamics | Noise control | Stochastic control theory | Studies | Mathematical analysis | Computational fluid dynamics | Stochastic processes | Optimal control | Differential equations | Schroedinger equation | Transport | Joints

60J60 | Mathematics | Theory of Computation | Optimal transport | 28A50 | Optimization | Schrödinger bridge | 49L20 | 49J20 | Calculus of Variations and Optimal Control; Optimization | 35Q35 | Stochastic control | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | MATHEMATICS, APPLIED | Schrodinger bridge | MECHANICS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FLUID | TERMS | QUANTUM-THEORY | Bridges | Fluid dynamics | Noise control | Stochastic control theory | Studies | Mathematical analysis | Computational fluid dynamics | Stochastic processes | Optimal control | Differential equations | Schroedinger equation | Transport | Joints

Journal Article

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2018, Volume 56, Issue 2, pp. 1038 - 1057

We propose a general framework for studying the optimal impulse control problem in the presence of uncertainty on the parameters. Given a prior on the...

Bayesian filtering | Uncertainty | Optimal control | MATHEMATICS, APPLIED | optimal control | uncertainty | AUTOMATION & CONTROL SYSTEMS | Probability | Mathematics

Bayesian filtering | Uncertainty | Optimal control | MATHEMATICS, APPLIED | optimal control | uncertainty | AUTOMATION & CONTROL SYSTEMS | Probability | Mathematics

Journal Article

11.
Full Text
On the asymptotic optimality of greedy index heuristics for multi-action restless bandits

Advances in Applied Probability, ISSN 0001-8678, 09/2015, Volume 47, Issue 3, pp. 652 - 667

The class of restless bandits as proposed by Whittle (1988) have long been known to be intractable. This paper presents an optimality result which extends that...

49M20 | 90C40 | 49L20 | 93E20 | multi-action restless bandit | asymptotic optimality | Index heuristic | stochastic resource allocation

49M20 | 90C40 | 49L20 | 93E20 | multi-action restless bandit | asymptotic optimality | Index heuristic | stochastic resource allocation

Journal Article

Journal of Applied Probability, ISSN 0021-9002, 09/2015, Volume 52, Issue 3, pp. 718 - 735

In a defaultable market, an investor trades having only partial information about the behavior of the market. Taking into account the intraday stock movements,...

93E11 | Optimal investment | 49L20 | 93E03 | dynamic programming | default time | exponential utility | filtering | backward stochastic differential equation

93E11 | Optimal investment | 49L20 | 93E03 | dynamic programming | default time | exponential utility | filtering | backward stochastic differential equation

Journal Article

Acta Mathematica Scientia, ISSN 0252-9602, 5/2019, Volume 39, Issue 3, pp. 857 - 873

This article is devoted to the study of fully nonlinear stochastic Hamilton-Jacobi (HJ) equations for the optimal stochastic control problem of ordinary...

backward stochastic partial differential equation | viscosity solution | 49L20 | 93E20 | Analysis | Stochastic Hamilton-Jacobi equation | optimal stochastic control | Mathematics, general | 35D40 | Mathematics | 49L25 | 60H15

backward stochastic partial differential equation | viscosity solution | 49L20 | 93E20 | Analysis | Stochastic Hamilton-Jacobi equation | optimal stochastic control | Mathematics, general | 35D40 | Mathematics | 49L25 | 60H15

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 04/2017, Volume 127, Issue 4, pp. 1171 - 1203

We design an importance sampling scheme for backward stochastic differential equations (BSDEs) that minimizes the conditional variance occurring in...

Backward stochastic differential equations | Empirical regressions | Importance sampling | 49L20 | 65C30 | 93E24 | 60H07 | 62Jxx | STATISTICS & PROBABILITY | VARIANCE | Analysis | Algorithms | Differential equations

Backward stochastic differential equations | Empirical regressions | Importance sampling | 49L20 | 65C30 | 93E24 | 60H07 | 62Jxx | STATISTICS & PROBABILITY | VARIANCE | Analysis | Algorithms | Differential equations

Journal Article

15.
Full Text
Experimental Results of Optimal and Robust Control for Uncertain Linear Time-Delay Systems

Journal of Optimization Theory and Applications, ISSN 0022-3239, 2018, Volume 181, Issue 3, pp. 1076 - 1089

This paper addresses the issue of the regulation of the dehydration air temperature in a dryer. The classical optimization approach is used to solve the...

Time-delay systems | Lyapunov redesign | Optimal control | Experimental results | MATHEMATICS, APPLIED | DESIGN | INPUT | STATE | GUARANTEED COST CONTROL | 49L20 | 93D21 | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | 93C95 | 93C83 | Time delay systems | Dehydration | Linear control | Delay | Redesign | Robust control | Robustness (mathematics) | Production planning | Air temperature | Control algorithms | Control theory | Linearization

Time-delay systems | Lyapunov redesign | Optimal control | Experimental results | MATHEMATICS, APPLIED | DESIGN | INPUT | STATE | GUARANTEED COST CONTROL | 49L20 | 93D21 | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | 93C95 | 93C83 | Time delay systems | Dehydration | Linear control | Delay | Redesign | Robust control | Robustness (mathematics) | Production planning | Air temperature | Control algorithms | Control theory | Linearization

Journal Article

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2016, Volume 54, Issue 2, pp. 1017 - 1029

In this note, we propose two different approaches to rigorously justify a pseudo-Markov property for controlled diffusion processes which is often (explicitly...

Dynamic programming principle | Stochastic control | Pseudo-Markov property | Martingale problem | Probability | Mathematics

Dynamic programming principle | Stochastic control | Pseudo-Markov property | Martingale problem | Probability | Mathematics

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 10/2019, Volume 113, Issue 4, pp. 3635 - 3647

In this paper, by using a recent fixed point theorem, we study the existence and uniqueness of positive solutions for the following m-point fractional boundary...

m-point fractional boundary value problem | 47H10 | 49L20 | Fixed point theorem | Theoretical, Mathematical and Computational Physics | Positive solution | Mathematics, general | Mathematics | Applications of Mathematics

m-point fractional boundary value problem | 47H10 | 49L20 | Fixed point theorem | Theoretical, Mathematical and Computational Physics | Positive solution | Mathematics, general | Mathematics | Applications of Mathematics

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2018, Volume 370, Issue 3, pp. 2115 - 2160

We analyze a stochastic optimal control problem, where the state process follows a McKean-Vlasov dynamics and the diffusion coefficient can be degenerate. We...

Dynamic programming principle | Controlled McKean-Vlasov stochastic differential equations | Randomization method | Forward-backward stochastic differential equations | MATHEMATICS | STOCHASTIC DIFFERENTIAL-EQUATIONS | dynamic programming principle | BACKWARD SDE REPRESENTATION | randomization method | MEAN-FIELD GAMES | forward-backward stochastic differential equations

Dynamic programming principle | Controlled McKean-Vlasov stochastic differential equations | Randomization method | Forward-backward stochastic differential equations | MATHEMATICS | STOCHASTIC DIFFERENTIAL-EQUATIONS | dynamic programming principle | BACKWARD SDE REPRESENTATION | randomization method | MEAN-FIELD GAMES | forward-backward stochastic differential equations

Journal Article

Dynamical Systems, ISSN 1468-9367, 10/2019, Volume 34, Issue 4, pp. 685 - 709

We study a skew product IFS on the cylinder defined by Baker-like maps associated to a finite family of potential functions and the doubling map. We show that...

discounted ergodic averages | 37-XX | Bellman equation | 28Dxx | dynamic programming | 90C39 | ergodic theory | 37Hxx | 37L40 | ergodic optimization | SRB measures | Iterated function system | 49Lxx | 49L20 | 37B10 | 37B55 | MATHEMATICS, APPLIED | MATHER | MINIMIZING MEASURES | PHYSICS, MATHEMATICAL | PRINCIPLES | Maximization | Maps | Invariants | Optimization | Ergodic processes | Cylinders

discounted ergodic averages | 37-XX | Bellman equation | 28Dxx | dynamic programming | 90C39 | ergodic theory | 37Hxx | 37L40 | ergodic optimization | SRB measures | Iterated function system | 49Lxx | 49L20 | 37B10 | 37B55 | MATHEMATICS, APPLIED | MATHER | MINIMIZING MEASURES | PHYSICS, MATHEMATICAL | PRINCIPLES | Maximization | Maps | Invariants | Optimization | Ergodic processes | Cylinders

Journal Article

ANNALS OF APPLIED PROBABILITY, ISSN 1050-5164, 02/2018, Volume 28, Issue 1, pp. 1 - 34

In this paper, we aim to develop the stochastic control theory of branching diffusion processes where both the movement and the reproduction of the particles...

VISCOSITY SOLUTIONS | viscosity solution | dynamic programming principle | Hamilton-Jacobi-Bellman equation | branching diffusion process | CONSTRUCTION | Stochastic control | STATISTICS & PROBABILITY

VISCOSITY SOLUTIONS | viscosity solution | dynamic programming principle | Hamilton-Jacobi-Bellman equation | branching diffusion process | CONSTRUCTION | Stochastic control | STATISTICS & PROBABILITY

Journal Article

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