检索结果-内蒙古大学图书馆

Markov decision processes under model uncertainty

MATHEMATICAL FINANCE 2023年第3期33卷 618-665页

作者： Neufeld, Ariel Sester, Julian Sikic, Mario NTU Singapore Div Math Sci Singapore Singapore Natl Univ Singapore Dept Math Singapore Singapore Univ Zurich Dept Banking & Finance Zurich Switzerland NTU Singapore Div Math Sci 21 Nanyang Link Singapore 637371 Singapore

We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle, we obtain a local-to-global paradigm, namely solving a local, that is, a one time-step robust optimization problem leads to an optimizer of the global (i.e., infinite time-steps) robust stochastic optimal control problem, as well as to a corresponding worst-case measure. Moreover, we apply this framework to portfolio optimization involving data of the S&P500$S\&P\nobreakspace 500$. We present two different types of ambiguity sets;one is fully data-driven given by a Wasserstein-ball around the empirical measure, the second one is described by a parametric set of multivariate normal distributions, where the corresponding uncertainty sets of the parameters are estimated from the data. It turns out that in scenarios where the market is volatile or bearish, the optimal portfolio strategies from the corresponding robust optimization problem outperforms the ones without model uncertainty, showcasing the importance of taking model uncertainty into account.

关键词： ambiguity dynamic programming principle Markov decision problem portfolio optimization

来源：评论

学校读者我要写书评

暂无评论

Deep-Control of Memory via Stochastic Optimal Control and Deep Learning 4th

Deep-Control of Memory via Stochastic Optimal Control and De...

引用

International Conference on Mathematics and its Applications in Science and Engineering (ICMASE)

作者： Savku, Emel Univ Oslo Dept Math Oslo Norway

ISBN: (纸本)9783031492204;9783031492181;9783031492174

In this survey work, we introduce Stochastic Differential Delay Equations and their impacts on Stochastic Optimal Control problems. We observe time delay in the dynamics of a state process that may correspond to inertia or memory in a financial system. For such systems, we demonstrate two special approaches to handle delayed control problems by applying the dynamic programming principle. Moreover, we clarify the technical challenges rising as a consequence of the conflict between the path-dependent, infinite-dimensional nature of the problem and the necessity of the Markov property. Furthermore, we present two different Deep Learning algorithms to solve targeted delayed control tasks and illustrate the results for a complete memory portfolio optimization problem.

关键词： dynamic programming principle Feedforward neural networks Financial engineering Long-short term memory Stochastic optimal control Time delay

来源：评论

学校读者我要写书评

暂无评论

Neural networks for first order HJB equations and application to front propagation with obstacle terms

引用

PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS 2023年第5期4卷 1-36页

作者： Bokanowski, Olivier Prost, Averil Warin, Xavier Univ Paris Cite Lab Jacques Louis Lions LJLL F-75013 Paris France Sorbonne Univ CNRS LJLL F-75005 Paris France Normandie Univ INSA Rouen Normandie LMI UR 3226 F-76000 Rouen France EDF R&D F-91120 Palaiseau France FiME F-91120 Palaiseau France

We consider a deterministic optimal control problem, focusing on a finite horizon scenario. Our proposal involves employing deep neural network approximations to capture Bellman's dynamic programming principle. This also corresponds to solving first-order Hamilton-Jacobi-Bellman (HJB) equations. Our work builds upon the research conducted by Hur & eacute;et al. (SIAM J Numer Anal 59(1):525-557, 2021), which primarily focused on stochastic contexts. However, our objective is to develop a completely novel approach specifically designed to address error propagation in the absence of diffusion in the dynamics of the system. Our analysis provides precise error estimates in terms of an average norm. Furthermore, we provide several academic numerical examples that pertain to front propagation models incorporating obstacle constraints, demonstrating the effectiveness of our approach for systems with moderate dimensions (e.g., ranging from 2 to 8) and for nonsmooth value functions.

关键词： Neural networks Deterministic optimal control dynamic programming principle First order Hamilton-Jacobi-Bellman equation State constraints

来源：评论

学校读者我要写书评

暂无评论

dynamic Set Values for Nonzero-Sum Games with Multiple Equilibriums

引用

MATHEMATICS OF OPERATIONS RESEARCH 2022年第1期47卷 616-642页

作者： Feinstein, Zachary Rudloff, Birgit Zhang, Jianfeng Stevens Inst Technol Sch Business Hoboken NJ 07030 USA Vienna Univ Econ & Business Inst Stat & Math A-1020 Vienna Austria Univ Southern Calif Dept Math Los Angeles CA 90089 USA

Nonzero sum games typically have multiple Nash equilibriums (or no equilibrium), and unlike the zero-sum case, they may have different values at different equilibriums. Instead of focusing on the existence of individual equilibriums, we study the set of values over all equilibriums, which we call the set value of the game. The set value is unique by nature and always exists (with possible value 0). Similar to the standard value function in control literature, it enjoys many nice properties, such as regularity, stability, and more importantly, the dynamic programming principle. There are two main features in order to obtain the dynamic programming principle: (i) we must use closed-loop controls (instead of open-loop controls);and (ii) we must allow for path dependent controls, even if the problem is in a state-dependent (Markovian) setting. We shall consider both discrete and continuous time models with finite time horizon. For the latter, we will also provide a duality approach through certain standard PDE (or path-dependent PDE), which is quite efficient for numerically computing the set value of the game.

关键词： nonzero sum game Nash equilibrium set value dynamic programming principle closed-loop controls path dependent PDE

来源：评论

学校读者我要写书评

暂无评论

Risk-sensitive optimal stopping with unbounded terminal cost function

引用

ELECTRONIC JOURNAL OF PROBABILITY 2022年第none期27卷 1-30页

作者： Jelito, Damian Stettner, Lukasz Jagiellonian Univ Inst Math Krakow Poland Polish Acad Sci Inst Math Warsaw Poland

In this paper we consider an infinite time horizon risk-sensitive optimal stopping problem for a Feller-Markov process with an unbounded terminal cost function. We show that in the unbounded case an associated Bellman equation may have multiple solutions and we give a probabilistic interpretation for the minimal and the maximal one. Also, we show how to approximate them using finite time horizon problems. The analysis, covering both discrete and continuous time case, is supported with illustrative examples.

关键词： optimal stopping Feller-Markov process Bellman equation dynamic programming principle unbounded cost function

来源：评论

学校读者我要写书评

暂无评论

dynamic programming principle FOR TUG-OF-WAR GAMES WITH NOISE

引用

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS 2012年第1期18卷 81-90页

作者： Manfredi, Juan J. Parviainen, Mikko Rossi, Julio D. Univ Pittsburgh Dept Math Pittsburgh PA 15260 USA Helsinki Univ Technol Inst Math Helsinki 02015 Finland FCEyN UBA 1428 Dept Matemat Buenos Aires DF Argentina

We consider a two-player zero-sum-game in a bounded open domain Omega described as follows: at a point x epsilon Omega, Players I and II play an epsilon-step tug-of-war game with probability alpha, and with probability beta (alpha + beta = 1), a random point in the ball of radius epsilon centered at x is chosen. Once the game position reaches the boundary, Player II pays Player I the amount given by a fixed payoff function F. We give a detailed proof of the fact that the value functions of this game satisfy the dynamic programming principle u(x) -alpha/2 {sup u(y)(y is an element of(B) over bar epsilon(x)) + inf(y is an element of(B) over bar epsilon(x)) u(y)} + beta f(B epsilon(x)) u(y)dy, for x is an element of Omega with u( y) = F( y) when y is not an element of Omega. This principle implies the existence of quasioptimal Markovian strategies.

关键词： Dirichlet boundary conditions dynamic programming principle p-Laplacian stochastic games two-player zero-sum games

来源：评论

学校读者我要写书评

暂无评论

Erratum: The Robust Superreplication Problem: A dynamic Approach

引用

SIAM JOURNAL ON FINANCIAL MATHEMATICS 2022年第2期13卷 653-655页

作者： Carassus, Laurence Obloj, Jan Wiesel, Johannes Leonard de Vinci Pole Univ Res Ctr F-92916 Paris France Univ Reims LMR UMR 9008 F-51100 Reims France Univ Oxford Math Inst Oxford OX1 3JP England Univ Oxford St Johns Coll Oxford OX1 3JP England Columbia Univ Stat Dept New York NY 10027 USA

The assertions of Proposition 3.7 in our paper ``The robust superreplication problem: A dynamic approach"" [L. Carassus, J. Ob\lo'\j, and J. Wiesel, SIAM J. Financial Math., 10 (2019), pp. 907--941] may ... 详细信息

关键词： robust pricing and hedging superhedging dynamic programming principle concave envelope dynamic robust approach

来源：评论

学校读者我要写书评

暂无评论

Mathematical modelling and optimal control analysis of pandemic dynamics as a hybrid system

引用

EUROPEAN JOURNAL OF CONTROL 2024年 75卷

作者： Dharmatti, Sheetal Krishnan, Nandakishor IISER Thiruvananthapuram Sch Math Maruthamala PO Trivandrum 695551 Kerala India Eotvos Lorand Univ Inst Biol Doctoral Sch Biol Pazmany Peter Setany 1-C HU-1117 Budapest Hungary Ctr Ecol Res Inst Evolut Konkoly Thege Mikl Ut HU-1121 Budapest Hungary

The study of epidemics using mathematical modelling is critical in understanding its dynamics and proposing potential control measures. We propose a generalised epidemiological model corresponding to a pandemic wherein its dynamics is represented as a novel hybrid system obtained by coupling a deterministic model with a stochastic model. The hybrid system dynamics is established in individualistic (macroscopic) and intraindividualistic (microscopic) scales. The established hybrid system is then considered the basis for an optimal control problem, with the rate of vaccination and velocity of spatial dynamics taken as the control parameters affecting the system's trajectory. We define the cost functional constituted by the continuous cost corresponding to the deterministic model and discrete costs corresponding to the transitions in the microscopic scale. The objective of the control problem is to find an optimal control pair of vaccination rate and spatial velocity, which minimises the cost functional. We use the dynamic programming principle (DPP) as the optimisation technique, followed by verification of the value function obtained by DPP as a viscosity solution of the appropriate Hamilton-Jacobi-Bellman equation to analyse the existence of an optimal control pair to the hybrid system. We prove the existence of optimal controls to the multi -scale dynamics for pandemic modelling, along with an abstract method to synthesise it.

关键词： Population dynamics Stochastic population model Hybrid control dynamic programming principle Viscosity solution

来源：评论

学校读者我要写书评

暂无评论

dynamic programming principle FOR STOCHASTIC RECURSIVE OPTIMAL CONTROL PROBLEM WITH DELAYED SYSTEMS

引用

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS 2012年第4期18卷 1005-1026页

作者： Chen, Li Wu, Zhen China Univ Min & Technol Dept Math Beijing 100083 Peoples R China Shandong Univ Sch Math Jinan 250100 Peoples R China

In this paper, we study one kind of stochastic recursive optimal control problem for the systems described by stochastic differential equations with delay (SDDE). In our framework, not only the dynamics of the systems but also the recursive utility depend on the past path segment of the state process in a general form. We give the dynamic programming principle for this kind of optimal control problems and show that the value function is the viscosity solution of the corresponding infinite dimensional Hamilton-Jacobi-Bellman partial differential equation.

关键词： Stochastic differential equation with delay recursive optimal control problem dynamic programming principle Hamilton-Jacobi-Bellman equation

来源：评论

学校读者我要写书评

暂无评论

Optimal multidimensional reinsurance policies under a common shock dependency structure

引用

EUROPEAN ACTUARIAL JOURNAL 2022年第2期12卷 559-577页

作者： Azarbad, M. Parham, G. A. Alavi, S. M. R. Shahid Chamran Univ Ahvaz Fac Math Sci & Comp Dept Stat Ahvaz Iran

In this paper, we consider an insurance company that is active in multiple dependent lines. We assume that the risk process in each line is a Cramer-Lundberg process. We use a common shock dependency structure to consider the possibility of simultaneous claims in different lines. According to a vector of reinsurance strategies, the insurer transfers some part of its risk to a reinsurance company. Our goal is to maximize our objective function (expected discounted surplus level integrated over time) using a dynamic programming method. The optimal objective function (value function) is characterized as the unique solution of the corresponding Hamilton-Jacobi-Bellman equation with some boundary conditions. Moreover, an algorithm is proposed to numerically obtain the optimal solution of the objective function, which corresponds to the optimal reinsurance strategies.

关键词： Cramer-Lundberg process Common shock dynamic programming principle Reinsurance

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：