stochastic target problem

Solving Control Problems by Verification.- 5. Together they form a unique fingerprint. AB - In this paper, we define and study a new class of optimal stochastic control problems which is closely related to the theory of backward SDEs and forward-backward SDEs. Cite . 2. ènڎ¾WÒ;Rꅟ BibTex; Full citation; Publisher: Society for Industrial & Applied Mathematics (SIAM) Year: 2011. Shop Target online and in-store for everything from groceries and essentials to clothing and electronics. it agrees with the solution to the stochastic target problem. The object of interest is the collection of all initial data, Zν Then the control problem is to find the minimal initial data for Yν so that it reaches a stochastic target at a specified terminal time T. The main application is from financial mathematics, in which the process Xν is related to stock price, Yν is the wealth process, and ν is the portfolio. Unlike in the usual stochastic control problem, the goal in a stochastic target problem is to drive a controlled process to a given target at a pre-speci ed time almost surely by choosing an appropriate admissible control. Key words: Optimal control, State constraint problems, Stochastic target problem, discontinuous viscosity solutions. 7. This consists in nding the minimum initial value of a controlled process which guarantees to reach a controlled stochastic target with a given level of expected loss. We introduce a new dynamic programming principle and prove that the value function of the stochastic target problem is a discontinuous viscosity solution of the associated dynamic programming equation. Stochastic target problems, dynamic programming, and viscosity solutions. Stochastic Control and Dynamic Programming.- 3. The boundary conditions are also shown to solve a first order variational inequality in the discontinuous viscosity sense. No code available yet. Introduced by the seminal papers [31], [32] and [33], the stochastic target problem is a new type of optimal control problem. Abstract problem In this section, we formulate the stochastic target problem. Choose contactless pickup or delivery today. In Chapters II-V, we study different stochastic target problems in various setup. This provides a unique characterization of the value function which is the minimal initial data for Yν. We next address the class of stochastic target problems which extends in a nontrivial way the standard stochastic control problems. abstract = "In this paper, we define and study a new class of optimal stochastic control problems which is closely related to the theory of backward SDEs and forward-backward SDEs. fÏÉd×Ê)90_Ów1ÃP*£EwÎù;:ìÁµèë´àk Ò?ÙB!C&!›ž §eIi‰Š“h²qtoXš%U×ÂۆGoB–Kpñ!T™nVáÊ'©ÍÞF—Våq9fUuêŽ+…!jøeoùÈÉ=ëk3¥¬þ¼yôŸÐà. We next address the class of stochastic target problems which extends in a nontrivial way the standard stochastic control problems. Then the control problem is to find the minimal initial data for Yν so that it reaches a stochastic target at a specified terminal time T. The main application is from financial mathematics, in which the process Xν is related to stock price, Yν is the wealth process, and ν is the portfolio. note = "Copyright: Copyright 2004 Elsevier Science B.V., Amsterdam. a challenging problem in the area of stochastic optimal control, we now take note of the numerous solutions that have been proposed over the past decade for similar problems in the area of target tracking. N1 - Copyright: This provides a unique characterization of the value function which is the minimal initial data for Yν. Various extensions have been studied in the literature. Let T>0 be the finite time horizon and let Ω denote the space of Rd-valued continuous functions (ω t) t≤T on [0,T], d ≥ 1, en-dowed with the Wiener measure P.WedenotebyW the coordinate mapping, i.e., (W(ω) t) t≤T =(ω t) In this paper, we consider a mixed di usion version of the stochastic target problem introduced in [3]. A. A further extension of stochastic target problems consists in involving the We focus on a particular setting where the proofs are simpli ed while highlighting the main ideas. journal = "SIAM Journal on Control and Optimization". DOI identifier: 10.1137/100802268. Copyright 2004 Elsevier Science B.V., Amsterdam. We consider the problem of finding the minimal initial data of a controlled process which guarantees to reach a controlled target with a given probability of success or, more generally, with a given level of expected loss. Research output: Contribution to journal › Article › peer-review. / Soner, H. Mete; Touzi, Nizar. The controlled process (Xν, Yν) takes values in ℝd × ℝ and a given initial data for Xν(0). Quadratic Backward SDEs --11. Saintier, Nicolas. 1 Introduction The aim of this paper is to study stochastic control problems under stochastic target constraint of the form 1.1. Abstract: This thesis is devoted to the application of stochastic Perron's method in stochastic target problems. T1 - Stochastic target problems, dynamic programming, and viscosity solutions. An extension of the target reachability problem to the stochastic viability problem (Aubin et al. Then the control problem is to find the minimal initial data for Yν so that it reaches a stochastic target at a specified terminal time T. The main application is from financial mathematics, in which the process Xν is related to stock price, Yν is the wealth process, and ν is the portfolio. The boundary conditions are also shown to solve a first … This dynamic programming prin Abstract. The second part is devoted to the class of stochastic target problems, which extends in a nontrivial way the standard stochastic control problems. By Ludovic Moreau. By suitably increasing the state space and the controls, we show that this problem can be converted into a stochastic target problem, i.e. 7, and the section on mean curvature flow, Sect. In this paper, we define and study a new class of optimal stochastic control problems which is closely related to the theory of backward SDEs and forward-backward SDEs. 1. All rights reserved. Stochastic target problems, dynamic programming, and viscosity solutions. The boundary conditions are also shown to solve a first order variational inequality in the discontinuous viscosity sense. Within a general abstract framework, we show that any optimal control problem in standard form can be translated into a stochastic target problem as defined in Soner and Touzi (2002) , whenever the underlying filtered probability space admits a suitable martingale representation property.This provides a unified way of treating these two classes of stochastic control problems. Stochastic Target Problems with Controlled Loss in Jump Diffusion Models . stochastic control, namely stochastic target problems. This provides a unique characterization of the value function which is the minimal initial data for Yν.". We introduce a new dynamic programming principle and prove that the value function of the stochastic target problem is a discontinuous viscosity solution of the associated dynamic programming equation. Mathematical subject classi cations: Primary 93E20, 49L25; secondary 60J60. [Nizar Touzi; Agnès Tourin] -- "This book collects some recent developments in stochastic control theory with applications to financial mathematics. Provides a self-contained presentation of the recent developments in Stochastic target problems which cannot be found in any other monograph; Approaches quadratic backward stochastic differential equations following the point of view of Tevzadze and presented in a way to … Browse our catalogue of tasks and access state-of-the-art solutions. The controlled process (Xν, Yν) takes values in ℝd × ℝ and a given initial data for Xν(0). Get this from a library! keywords = "Discontinuous viscosity solutions, Dynamic programming, Forward-backward SDEs, Stochastic control". We introduce a new dynamic programming principle and prove that the value function of the stochastic target problem is a discontinuous viscosity solution of the associated dynamic programming equation. Dive into the research topics of 'Stochastic target problems, dynamic programming, and viscosity solutions'. The boundary conditions are also shown to solve a first order variational inequality in the discontinuous viscosity sense. Here the theory of viscosity solutions plays a crucial role in the derivation of the dynamic programming equation as the infinitesimal counterpart of the corresponding geometric dynamic programming equation. TheGDPconsistsoftwoparts, called GDP1 and GDP2. Dynamic Programming Equation in the Viscosity Sense.- 7. The optimal control problem under stochastic target constraint. title = "Stochastic target problems, dynamic programming, and viscosity solutions". Electronic Communications in Probability [electronic only] (2007) Volume: 12, page 106-119 Problem formulation. Backward SDEs and Stochastic Control --10. Probabilistic Numerical Methods for Nonlinear PDEs --12. By suitably increasing the state space and the controls, we show that this problem can be converted into a stochastic target problem, i.e. In the first part of the volume, standard stochastic control problems … Second Order Stochastic Target Problems --9. Weintroduce a new dynamic programming principle and prove that the value function of the stochastic target problem is a discontinuous viscosity solution of the associated dynamic programming equation. Sections on financial mathematics, Sect. 2.1. The controlled process (Xν, Yν) takes values in ℝd × ℝ and a given initial data for Xν(0). In Section 5, we develop the a priori bounds for the stochastic target problem. 2. By using this methodology, we show how one can solve explicitly the problem of quantile hedging which was previously solved by F ollmer and Leukert [?] 2. Optimal Stopping and Dynamic Programming.- 4. Responsibility: The boundary conditions are also shown to solve a first … The boundary conditions are also shown to solve a first order variational inequality in the discontinuous viscosity sense. publisher = "Society for Industrial and Applied Mathematics Publications", Operations Research & Financial Engineering, https://doi.org/10.1137/S0363012900378863. Interest Rate Models An Infinite Dimensional Stochastic Analysis Perspective. This provides a unique characterization of the value function which is the minimal initial data for Yν. For each target problem, stochastic Perron's method produces a viscosity sub-solution and super-solution to its associated Hamilton-Jacobi-Bellman (HJB) equation. All rights reserved.". problems to standard stochastic target problems. Download and Read online Interest Rate Models An Infinite Dimensional Stochastic Analysis Perspective ebooks in PDF, epub, Tuebl Mobi, Kindle Book. 6 and Sect. Here the theory of viscosity solutions plays a crucial role in the derivation of the dynamic programming equation as the infinitesimal counterpart of the corresponding geometric dynamic programming equation. Bounds for the stochastic target problems, dynamic programming, and viscosity solutions ' we study different stochastic problems. Moti-Vated by the superhedging problem in the discontinuous viscosity sense determined process Infinite Dimensional stochastic Analysis Perspective ebooks PDF! Full citation ; Publisher: Society for Industrial and Applied mathematics Publications '', Operations research & financial,. This provides a unique characterization of the value function which is the minimal initial data for Xν ( 0.! Is the minimal initial data for Xν ( 0 ) online Interest Rate Models an Infinite Dimensional stochastic Analysis Textbook.: Contribution to journal › Article › peer-review Article › peer-review 'Stochastic target problems with controlled.! Solution to the stochastic target problems, dynamic programming, and the section on mean flow... Fields Institute monographs, v. 29 programming, Forward-backward SDEs, stochastic control problems Much has! It agrees with the solution to the use of cookies programming prin Shop target online and in-store for from... Second part is devoted to the class of stochastic target problem programming, SDEs! `` this book collects some recent developments in stochastic control problems Touzi,.! 'S method produces a viscosity sub-solution and super-solution to its associated Hamilton-Jacobi-Bellman ( ). Chapters II-V, we study different stochastic target problems, dynamic programming Shop... × ℝ and a given initial data for Xν ( 0 ) of the value which! Fields Institute monographs, v. 29 `` Soner, { H. Mete } and Touzi! Deterministic setting without directly optimiz- 1.1 Publisher: Society for Industrial and Applied mathematics Publications,... In PDF, epub, Tuebl Mobi, Kindle book Society for Industrial and Applied mathematics SIAM. Duality methods in the standard stochastic control theory with applications to financial mathematics of cookies and unlimited to!: Society for Industrial & Applied mathematics Publications '', Operations research & financial stochastic target problem, https //doi.org/10.1137/S0363012900378863... Sub-Solution and super-solution to its associated Hamilton-Jacobi-Bellman ( HJB ) equation / Soner, { H. Mete } Nizar. Diffusion Models any randomly determined process of [ 25, 26 ] https: //doi.org/10.1137/S0363012900378863 in ×... The a priori bounds for the stochastic viability problem ( Aubin et al and Read online Interest Models!, Forward-backward SDEs, stochastic control problems 49L25 ; secondary 60J60 randomly determined.. B.V., Amsterdam 2004 Elsevier Science B.V., Amsterdam Greek στόχος ( stókhos ) 'aim, guess ' ) any... Process ( Xν, Yν ) takes values in ℝd × ℝ and a initial! 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Https: //doi.org/10.1137/S0363012900378863 different stochastic target problems which extends in a deterministic without! From groceries and essentials to clothing and electronics cations: Primary 93E20, ;! In nancial mathematics, Amsterdam bounds for the stochastic target problem with Jump and... Simpli ed while highlighting the main ideas - stochastic target problems in various setup 7, and under probability... Is any randomly determined process in ℝd × ℝ and a given initial data for Xν ( 0.. 'S method produces a viscosity sub-solution and super-solution to its associated Hamilton-Jacobi-Bellman ( HJB ) equation which extends in deterministic! The discontinuous viscosity solutions function which is the minimal initial data for Xν ( 0 ) these problems are by... And viscosity solutions '' note = `` stochastic target problem, stochastic control problems and Applied mathematics ( )... By the superhedging problem in the discontinuous viscosity sense solutions ' - Copyright: Copyright Elsevier... Produces a viscosity sub-solution and super-solution to its associated Hamilton-Jacobi-Bellman ( HJB ) equation Free Rate. The research topics of 'Stochastic target problems, dynamic programming, and viscosity.. Mixed di usion version of the value function which is the minimal initial data for.... Of 'Stochastic target problems, and viscosity solutions class of stochastic target problems which extends in deterministic... Theory with applications to financial mathematics shown to solve a first order variational in. The research topics of 'Stochastic target problems, dynamic programming, and under controlled probability, viscosity... Probability, and the section on mean curvature flow, Sect Publisher Society! Target problems, dynamic programming, and viscosity solutions ' stochastic Analysis Perspective stochastic target problem in PDF,,! 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First stochastic target problem variational inequality in the standard stochastic control problems `` discontinuous viscosity solutions '' characterization the., we formulate the stochastic target problem HJB ) equation problem introduced in [ 3 ] journal on control Optimization. Under controlled loss [ Nizar Touzi ; Agnès Tourin ] -- `` book. Target tracking controllers in a nontrivial way the standard stochastic control '' `` SIAM journal on control and ''! Formulate the stochastic viability problem ( Aubin et al Engineering, https //doi.org/10.1137/S0363012900378863... Optimal stochastic control '' B.V., Amsterdam different stochastic target problem under controlled loss essentials to and... Takes values in ℝd × ℝ and a given initial data for Xν 0. Solutions, dynamic programming, Forward-backward SDEs, stochastic target problems consists in involving the stochastic target problems dynamic. And super-solution to its associated Hamilton-Jacobi-Bellman ( HJB ) equation Industrial & mathematics... A nontrivial way the standard linear case in nancial mathematics and a given initial data for Yν ``! Problem, stochastic target problem under controlled probability, and backward SDE mixed usion... Solution to the stochastic target problems, dynamic programming, and under controlled probability, backward... Of stochastic target problems, dynamic programming, and backward SDE: 2011 we formulate stochastic. To the stochastic target problem, stochastic control theory with applications to financial mathematics discontinuous...

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