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A dynamic programming APPROACH TO DISTRIBUTION-CONSTRAINED OPTIMAL STOPPING

ANNALS OF APPLIED PROBABILITY 2022年第3期32卷 1902-1928页

作者： Kallblad, Sigrid Royal Inst Technol Dept Math Stockholm Sweden

We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales enables us to transform the distributional constraint into an initial condition and view the problem as a stochastic control problem;we establish the corresponding dynamic programming principle. The method offers a systematic approach for solving the problem for general constraints and under weak assumptions on the cost function. In addition, we provide certain continuity results for the value of the problem viewed as a function of its distributional constraint.

关键词： Distribution-constrained optimal stopping measure-valued martingales dynamic programming principle optimal transport measurable selection

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dynamic programming approach to reflected backward stochastic differential equations

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ELECTRONIC JOURNAL OF PROBABILITY 2023年第none期28卷 1-20页

作者： Hun, O. Kim, Mun-Chol Kim, Kon-Gun Kim II Sung Univ Fac Math Pyongyang North Korea

By introducing a new type of minimality condition, this paper gives a novel approach to the reflected backward stochastic differential equations (RBSDEs) with cadlag obstacles. Our first step is to prove the dynamic programming principles for nonlinear optimal stopping problems with g-expectations. We then use the nonlinear DoobMeyer decomposition theorem for g-supermartingales to get the existence of the solution. With a new type of minimality condition, we prove a representation formula of solutions to RBSDEs, in an efficient way. Finally, we derive some a priori estimates and stability results.

关键词： reflected backward stochastic differential equation nonlinear optimal stopping dynamic programming principle g-supermartingale decomposition non-Skorohod-type minimality condition second order reflected backward stochastic differential equation

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Impact of government's support policy on decision-making of platform participants under ESG

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NORTH AMERICAN JOURNAL OF ECONOMICS AND FINANCE 2025年 75卷

作者： Li, Renzhong Fei, Chen Fei, Weiyin Univ Shanghai Sci & Technol Business Sch Shanghai 200093 Peoples R China Anhui Polytech Univ Sch Math Phys & Finance Wuhu 241000 Peoples R China

Blockchain-based token platform economy is a new branch of digital platform economics. Constructing a continuous time dynamic model of token platform economy, this paper analyzes what kind of ESG policy is appropriate for the government, meanwhile the token platform participants (developers, users and speculators) make optimal investments and decisions under ESG policy. Simulation result shows neutral ESG policy is optimal. Based on the given neutral ESG policy, we have done the research on ESG investment and decision strategies for platform participants. Our research shows that the tokens selling rate and efforts of green platform (ESG score greater than 0) developers are lower than the ones of brown platform (ESG score less than 0). Consequently, when developers' token retention is about half of the initial amount, users should invest more brown tokens. Speculators should invest brown tokens for developers' high token retention. Green token investments of speculators and users are needed in other cases. Next, the impact of the government's three ESG policies on the maturity or termination of the platform also been analyzed. An important conclusion occurred: the government's aggressive or conservative ESG policy cannot make the development of the green platform better;Therefore, we suggest a neutral ESG policy which means that the government could adopt high tax incentive and high tax burden on the green and brown platform while it is not necessary to implement the extra subsidy and punishment policy on the green and brown platform.

关键词： ESG policy Decision-making Blockchain Token platform economics dynamic programming principle

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Local regularity estimates for general discrete dynamic programming equations

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JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES 2022年 167卷 225-256页

作者： Arroyo, Angel Blanc, Pablo Parviainen, Mikko Univ Complutense Madrid Interdisciplinary Math Inst Dept Appl Math & Math Anal MOMAT Res Grp Madrid 28040 Spain Univ Jyvaskyla Dept Math & Stat POB 35 FI-40014 Jyvaskyla Finland

We obtain an analytic proof for asymptotic Holder estimate and Harnack's inequality for solutions to a discrete dynamic programming equation. The results also generalize to functions satisfying Pucci-type inequalities for discrete extremal operators. Thus the results cover a quite general class of equations.(c) 2022 The Author(s). Published by Elsevier Masson SAS. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).

关键词： ABP-estimate dynamic programming principle Harnack?s inequality Local H?lder estimate Tug-of-war with noise Elliptic non-divergence form partial differential equation with bounded and measurable coefficients

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Using Approximate dynamic programming for Estimating the Revenues of a Hydrogen-based High-Capacity Storage Device

Using Approximate Dynamic Programming for Estimating the Rev...

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IEEE Symposium on Adaptive dynamic programming and Reinforcement Learning (ADPRL)

作者： Francois-Lavet, Vincent Fonteneau, Raphael Ernst, Damien Univ Liege Dept Elect Engn & Comp Sci B-4000 Liege Belgium

ISBN: (纸本)9781479945528

This paper proposes a methodology to estimate the maximum revenue that can be generated by a company that operates a high-capacity storage device to buy or sell electricity on the day-ahead electricity market. The methodology exploits the dynamic programming (DP) principle and is specified for hydrogen-based storage devices that use electrolysis to produce hydrogen and fuel cells to generate electricity from hydrogen. Experimental results are generated using historical data of energy prices on the Belgian market. They show how the storage capacity and other parameters of the storage device influence the optimal revenue. The main conclusion drawn from the experiments is that it may be advisable to invest in large storage tanks to exploit the inter-seasonal price fluctuations of electricity.

关键词： dynamic programming electrolysis fuel cells hydrogen storage power markets Belgian market day-ahead electricity market dynamic programming principle high-capacity storage device hydrogen-based storage devices interseasonal price fluctuations maximum revenue estimation optimal revenue dynamic programming Electricity Electrochemical processes Fuel cells Hydrogen Hydrogen storage

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ON THE TIME DISCRETIZATION OF STOCHASTIC OPTIMAL CONTROL PROBLEMS: THE dynamic programming APPROACH

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ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS 2019年第1期25卷 63-63页

作者： Bonnans, Joseph Frederic Gianatti, Justina Silva, Francisco J. Univ Paris Saclay CNRS Ctr Math Appl Ecole PolytechINRIA Saclay F-91128 Palaiseau France UNR CONICET CIFASIS Ctr Int Franco Argentino Ciencias Informa S2000EZP Rosario Argentina Univ Limoges Inst Rech XLIM DMI Fac Sci & Tech CNRSUMR 7252 F-87060 Limoges France

In this work, we consider the time discretization of stochastic optimal control problems. Under general assumptions on the data, we prove the convergence of the value functions associated with the discrete time problems to the value function of the original problem. Moreover, we prove that any sequence of optimal solutions of discrete problems is minimizing for the continuous one. As a consequence of the dynamic programming principle for the discrete problems, the minimizing sequence can be taken in discrete time feedback form.

关键词： Stochastic Control Discrete Time Systems dynamic programming principle Value Function Feedback Control

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NASH EQUILIBRIUM PAYOFFS FOR STOCHASTIC DIFFERENTIAL GAMES WITH REFLECTION

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ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS 2013年第4期19卷 1189-1208页

作者： Lin, Qian Univ Bielefeld Ctr Math Econ D-33501 Bielefeld Germany

In this paper, we investigate Nash equilibrium payoffs for nonzero-sum stochastic differential games with reflection. We obtain an existence theorem and a characterization theorem of Nash equilibrium payoffs for nonzero-sum stochastic differential games with nonlinear cost functionals defined by doubly controlled reflected backward stochastic differential equations.

关键词： Backward stochastic differential equations dynamic programming principle Nash equilibrium payoffs stochastic differential games

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Stochastic Optimal Control of Stayed Cable Vibrations with Wide-Band Random Wind Excitation using Axial Support Motion

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ADVANCES IN STRUCTURAL ENGINEERING 2015年第9期18卷 1535-1550页

作者： Fu, Bing Wang, Zhenyu Zhao, Yan Yang, Liu Shenyang Jianzhu Univ Sch Civil Engn Shenyang 110168 Peoples R China Zhejiang Univ Coll Civil Engn & Architecture Hangzhou 310058 Zhejiang Peoples R China

This paper proposes an optimal control strategy and corresponding method, to use the advantageous characteristics of the axial support motion to control the stayed cable vibrations in plane by wind excitation. Through a thorough investigation of wide-band random wind excitation and spatial relativity of the wind load along the cable, this study derives realistic and accurate motion equations of the control system. These motion equations are simplified into the form of the first four modes using the Galerkin method. The Ito stochastic differential equations of partial average for the system energy are derived using the stochastic averaging method of the quasi-integrable Hamiltonian systems. Furthermore, the dynamic programming equations with performance index are established by the stochastic dynamic programming principle. The random optimal control law is obtained by solving the dynamic programming equations using the approximate method. The numerical results show that, when standard deviations of the axial support motion are the same, the reduction of the standard deviation of the cable acceleration, and the cable displacement under the stochastic optimal control (SOC) law proposed by this paper, is larger than that under bilinear (BL) control. The SOC method proposed in this paper provides better results than the BL method.

关键词： stayed cable stochastic optimal control dynamic programming principle stochastic averaging method Hamiltonian system

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AN ASYMPTOTIC MEAN VALUE CHARACTERIZATION FOR A CLASS OF NONLINEAR PARABOLIC EQUATIONS RELATED TO TUG-OF-WAR GAMES

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SIAM JOURNAL ON MATHEMATICAL ANALYSIS 2010年第5期42卷 2058-2081页

作者： Manfredi, Juan J. Parviainen, Mikko Rossi, Julio D. Univ Pittsburgh Dept Math Pittsburgh PA 15260 USA Aalto Univ Sch Sci & Technol FI-00076 Helsinki Finland Univ Alicante Dept Anal Matemat E-03080 Alicante Spain

We characterize solutions to the homogeneous parabolic p-Laplace equation u(t) - vertical bar del u|(2-p)Delta(p)u = (p - 2)Delta(infinity)u + Delta u in terms of an asymptotic mean value property. The results are connected with the analysis of tug-of-war games with noise in which the number of rounds is bounded. The value functions for these games approximate a solution to the PDE above when the parameter that controls the size of the possible steps goes to zero.

关键词： Dirichlet boundary conditions dynamic programming principle parabolic p-Laplacian parabolic mean value property stochastic games tug-of-war games with limited number of rounds viscosity solutions

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A Verification Theorem for Optimal Stopping Problems with Expectation Constraints (vol 79, pg 145, 2019)

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APPLIED MATHEMATICS AND OPTIMIZATION 2019年第1期79卷 179-180页

作者： Ankirchner, Stefan Klein, Maike Kruse, Thomas Univ Jena Inst Math Ernst Abbe Pl 2 D-07743 Jena Germany Univ Duisburg Essen Fac Math Thea Leymann Str 9 D-45127 Essen Germany

We consider the problem of optimally stopping a continuous-time process with a stopping time satisfying a given expectation cost constraint. We show, by introducing a new state variable, that one can transform the problem into an unconstrained control problem and hence obtain a dynamic programming principle. We characterize the value function in terms of the dynamic programming equation, which turns out to be an elliptic, fully non-linear partial differential equation of second order. We prove a classical verification theorem and illustrate its applicability with several examples.

关键词： Optimal stopping Expectation constraints dynamic programming principle Verification theorem

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