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Asset pricing with dynamic programming

Computational Economics 2007年第3-4期29卷 233-265页

作者： Grüne, Lars Semmler, Willi Mathematisches Institut Fakultät für Mathematik und Physik Universität Bayreuth 95440 Bayreuth Germany Schwartz Center for Economic Policy Analysis New School New York NY United States Center for Empirical Macroeconomics Bielefeld University Bielefeld Germany

The study of asset price characteristics of stochastic growth models such as the risk-free interest rate, equity premium, and the Sharpe-ratio has been limited by the lack of global and accurate methods to solve dynamic optimization models. In this paper, a stochastic version of a dynamic programming method with adaptive grid scheme is applied to compute the asset price characteristics of a stochastic growth model. The stochastic growth model is of the type as developed by [Brock and Mirman (1972), Journal of Economic Theory, 4, 479-513 and Brock (1979), Part I: The growth model (pp. 165-190). New York: Academic Press;The economies of information and uncertainty (pp. 165-192). Chicago: University of Chicago Press. (1982). It has become the baseline model in the stochastic dynamic general equilibrium literature. In a first step, in order to test our procedure, it is applied to this basic stochastic growth model for which the optimal consumption and asset prices can analytically be computed. Since, as shown, our method produces only negligible errors, as compared to the analytical solution, in a second step, we apply it to more elaborate stochastic growth models with adjustment costs and habit formation. In the latter model preferences are not time separable and past consumption acts as a constraint on current consumption. This model gives rise to an additional state variable. We here too apply our stochastic version of a dynamic programming method with adaptive grid scheme to compute the above mentioned asset price characteristics. We show that our method is very suitable to be used as solution technique for such models with more complicated decision structure. © Springer Science+Business Media, LLC 2006.

关键词： Adaptive grid Asset pricing stochastic dynamic programming stochastic growth models

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Approximate dynamic programming approach for process control

Approximate dynamic programming approach for process control

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IFAC Symposium on Advanced Control of Chemical Processes (ADCHEM)

作者： Lee, Jay H. Wong, Weechin Georgia Inst Technol Sch Chem & Biomol Engn Atlanta GA 30332 USA

We assess the potentials of the approximate dynamic programming (ADP) approach for process control, especially as a method to complement the model predictive control (MPC) approach. In the artificial intelligence (AI) and operations research (OR) research communities, ADP has recently seen significant activities as an effective method for solving Markov decision processes (MDPs), which represent a type of multi-stage decision problems under uncertainty. Process control problems are similar to MDPs with the key difference being the continuous state and action spaces as opposed to discrete ones. In addition, unlike in other popular ADP application areas like robotics or games, in process control applications first and foremost concern should be on the safety and economics of the on-going operation rather than on efficient learning. We explore different options within ADP design, such as the pre-decision state vs. post-decision state value function, parametric vs. nonparametric value function approximator, batch-mode vs. continuous-mode learning, and exploration vs. robustness. We argue that ADP possesses great potentials, especially for obtaining effective control policies for stochastic constrained nonlinear or linear systems and continually improving them towards optimality. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： stochastic process control stochastic dynamic programming Approximate dynamic programming Dual control Constrained control

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Balancing learning and economies of scale for adaptive clinical trials

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OPERATIONS RESEARCH FOR HEALTH CARE 2013年第3期2卷 42-51页

作者： Fleischhacker, Adam J. Zhao, Yao Univ Delaware Dept Business Adm Newark DE 19716 USA State Univ New Jersey Rutgers Univ Dept Supply Chain Management & Mkt Sci Newark NJ 07102 USA

Prior to the start of an adaptive clinical trial, demand for an investigational drug can be highly uncertain. Treatment length, recommended dosages, and forecasted patient recruitment can fluctuate in response to early trial results. While initial demand forecasts can be very wrong, the factors influencing future demand can be learned during the trial. To take advantage of this learning, intra-trial production and/or packaging can be leveraged, but this is done at the expense of scale economies. In this paper, we study the balance between learning and economies of scale for adaptive clinical trials. We characterize the optimal production (or packaging) decisions and through analytical and numerical studies, we develop insights on the impact of fixed costs, learning rates in terms of forecasting future demand, inventory overage costs, and inventory underage costs on the value of having intra-trial flexibility and on decisions regarding quantity and timing of drug supply. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Clinical trial supply stochastic dynamic programming Production planning

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The stochastic lake game: A numerical solution

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JOURNAL OF ECONOMIC dynamicS & CONTROL 2006年第9-10期30卷 1569-1587页

作者： Dechert, W. D. O'Donnell, S. I. Baylor Coll Med Childrens Nutr Res Ctr Houston TX 77030 USA Univ Wisconsin Madison WI 53706 USA

In this paper, we numerically solve a stochastic dynamic programming problem for the solution of a stochastic dynamic game for which there is a potential function. The players select a mean level of control. The state transition dynamics is a function of the current state of. the system and a multiplicative noise factor on the control variables of the players. The particular application is for lake water usage. The control variables are the levels of phosphorus discharged (typically by farmers) into the watershed of the lake, and the random shock is the rainfall that washes the phosphorus into the lake. The state of the system is the accumulated level of phosphorus in the lake. The system dynamics are sufficiently nonlinear so that there can be two Nash equilibria. A Skiba-like point can be present in the optimal control solution. We analyze (numerically) how the dynamics and the Skiba-like point change as the variance of the noise (the rain) increases. The numerical analysis uses a result of Dechert (1978. Optimal control problems from second order difference equations. Journal of Economic Theory 19, 50-63) to construct a potential function for the dynamic game. This greatly reduces the computational burden in finding Nash equilibria solutions for the dynamic game. (c) 2006 Elsevier B.V. All rights reserved.

关键词： stochastic optimal control Markov processes stochastic dynamic programming lake water pollution dynamic games with a potential function

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Optimal production control under uncertainty with revenue management considerations

Optimal production control under uncertainty with revenue ma...

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作者： Ceryan, Oben University of Michigan

学位级别：Ph.D.

This dissertation consists of three essays on supply chain and revenue management. Its main focus is the integration of dynamic production and demand management decisions for multiple products facing uncertain demand. The study considers three problem settings to inquire into flexibility's influence on a dynamic pricing strategy, managing exogenous demand for intermediary products, and allocation of shared resources among multiple products in a make-to-order environment. The first chapter studies a joint mechanism of dynamic pricing and capacity flexibility to mitigate demand and supply mismatches. We consider a firm producing two substitutable products with price-correlated demands utilizing capacitated product-dedicated and flexible resources. We characterize the structure and sensitivity of the optimal production and pricing decisions and find that the existence of a flexible resource in the firm's capacity portfolio helps maintain stable price differences across items over time. This result has favorable ramifications from a marketing standpoint as it suggests that even when a firm applies a dynamic pricing strategy, it may still establish consistent price positioning among multiple products if it can employ a flexible replenishment resource. We also investigate the economic benefits of a joint strategy versus applying each tool individually. The second chapter considers a setting where a single end-product is assembled from many intermediate components with external demand for the intermediate products as well as the end-product. We address the questions on how to decide on the production quantities for each component, when to initiate an assembly operation and how to set admission rules for demands targeted at various products. In addition to providing structural results for the optimal policy and its sensitivity to product revenues, we also extend the model to multiple customer classes and to settings with partial revenue collecting schemes. We propose a nove

关键词： dynamic Pricing Production Control stochastic dynamic programming Revenue Management Supply Chain Management Assemble-to-Order Systems Thesis

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An integrated framework for freight forwarders: Exploitation of dynamic information for multimodal transportation

An integrated framework for freight forwarders: Exploitation...

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作者： Azadian, Farshid Wayne State University

学位级别：Ph.D.

Advent of real-time information broadcasting technologies, growth in demand for air-cargo, and increased congestion and variability on air-road network, are the main forces compelling today's air-freight forwarders to improve their operational decision-making to be more competitive and responsive to needs of customers. This research studies the air-cargo transportation on both road (short-haul) and air (long haul) network from the perspective of a mid-size freight forwarder. We develop a routing algorithm for congestion avoidance on air-network based on historical data and introduce an innovative approach to incorporate real-time information to enable dynamic routing of cargo on a stochastic air-network. In the road network, we introduce a new class of pickup and delivery problems to carry out the customer load pickups, fleet management, cargo-to-flight assignments, and airport deliveries in a multiple airport region under alternative access airport policy. The main contributions of this research to the air-cargo literature are the study of the value of real-time information and introduction of the concept of dynamic air-cargo routing. In addition, this is the first study that provides an operational framework to implement the alternative access airport policy. This research also contributes to operations research and logistics literature by introducing a new class of pickup and deliveries with time-sensitive and pair-dependent cost structure. It also contributes an innovative algorithm based on successive subproblem solving for Lagrangian decomposed mixed integer programming that shows to be efficient in obtaining near optimal solutions in reasonable time. The performances of the algorithms presented in this research are tested through experimental and real-world case studies. The results demonstrate that dynamic routing with real-time information can dramatically improve delivery reliability and reduce expected cost on the air-network. Moreover, they confirm that

关键词： Air-cargo Transportation Alternative Access Airports Intelligent Transportation Systems Multimodal Transportation Pickup and Delivery Problems stochastic dynamic programming

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Incorporating drivability metrics into optimal energy management strategies for hybrid vehicles

Incorporating drivability metrics into optimal energy manage...

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作者： Opila, Daniel F. University of Michigan

学位级别：Ph.D.

Hybrid Vehicle fuel economy performance is highly sensitive to the "Energy Management" strategy used to regulate power flow among the various energy sources and sinks. Optimal solutions are easy to specify if the drive cycle is known a priori. It is very challenging to compute controllers that yield good fuel economy for a class of drive cycles representative of typical driver behavior. Additional challenges come in the form of constraints on powertrain activity, like shifting and starting the engine, which are commonly called "drivability" metrics. These constraints can adversely affect fuel economy. In this dissertation, drivability restrictions are included in a Shortest Path stochastic dynamic programming (SPSDP) formulation of the energy management problem to directly address this tradeoff and generate optimal, causal controllers. The controllers are evaluated on Ford Motor Company's highly accurate proprietary vehicle model and compared to a controller developed by Ford for a prototype vehicle. The SPSDP-based controllers improve fuel economy more than 15% compared to the industrial controller on government test cycles. In addition, the SPSDP-based controllers can directly quantify tradeoffs between fuel economy and drivability. Hundreds of thousands of simulations are conducted using real-world drive cycles to evaluate performance and robustness in the real world, demonstrating 10% improvement compared to the baseline. Finally, the controllers are tested in a real vehicle.

关键词： Hybrid Vehicles stochastic dynamic programming dynamic programming Optimal Control Energy Management HEV Thesis

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Wind Generation Scheduling with Pump Storage Unit by Collocation Method

Wind Generation Scheduling with Pump Storage Unit by Colloca...

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General Meeting of the IEEE-Power-and-Energy-Society

作者： Gao, Feng Hallam, Arne Yu, Chien-Ning ABB Inc Santa Clara CA 95050 USA Iowa State Univ Dept Econom Ames IA 50010 USA

ISBN: (纸本)9781424442409

Wind generation is currently undergoing the fastest rate of growth of any form of electricity generation in the world. Integration of wind power into systems could be problematic, however, due to availability and variability of wind supply. As a proven storage technology, pump storage may provide/absorb additional capacity so as to hedge against adverse situations. A scheduling software is needed to coordinate wind generation and pump storage units, given existing price and wind forecasting modules. This paper first implements a "Collocation Method" to solve a dispatching problem of wind and pump storage units, given the forecasting of future price and wind generation. Second, given that a pumping decision is discrete while generation dispatching is continuous, this paper uses a two-step strategy to solve a mixed-integer problem. Transition constraints are modeled based on the property of collocation method. Third, this paper uses real wind generation and real-time energy price data to simulate scheduling activities by the proposed model. A comparison of expected profits between wind only and wind plus pump storage unit is given.

关键词： Collocation Method Pump Storage Hydro Real Time Market stochastic dynamic programming Wind Generation

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Optimizing long-term hydro-power production using markov decision processes

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International Transactions in Operational Research 1996年第3-4期3.0卷 223-241页

作者： Lamond, B.F. Boukhtouta, A. Université Laval Québec Canada

Modelling the long-term operation of hydroelectric systems is one of the classic applications of Markov decision process (MDP). The computation of optimal policies, for MDP models, is usually done by dynamic programming (DP) on a discretized state space. A major difficulty arises when optimizing multi-reservoir systems, because the computational complexity of DP increases exponentially with the number of sites. This so-called ‘curse of dimensionality’ has so far restricted the applicability of DP to very small systems (2 or 3 sites). Practitioners have thus had to resort to other methodologies for the long-term planning, often at the expense of rigour, and without reliable error estimates. This paper surveys recent research of MDP computation, with application to hydro-power systems. Three main approaches are discussed: (i) discrete DP, (ii) numerical approximation of the expected future reward function, and (iii) analytic solution of the DP recursion. © 1996 Blackwell Publishing Ltd.

关键词： Hydro-power Markov decision processes Reservoir management stochastic dynamic programming stochastic optimization

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stochastic POPULATION FORECASTS AND THEIR USES

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INTERNATIONAL JOURNAL OF FORECASTING 1992年第3期8卷 385-391页

作者： TULJAPURKAR, S STANFORD UNIV MORRISON INST POPULAT & RESOURCE STUDIESSTANFORDCA 94305

The properties and uses of stochastic forecasts are discussed here. For linear stochastic projections, we show how the computation of forecast moments and the statistical distribution of forecasts depend on the multiplicative and autoregressive structure of the dynamics. Both scalar and vector projection methods are discussed, and their similarities are explored. Next we discuss the uses of stochastic forecasts, arguing that it is important to relate forecasts to the specific decision-making criteria of particular forecast users. The example of Social Security is used to show how a dynamic programming approach may be used to explore alternative decisions in a probabilistic context.

关键词： stochastic POPULATION FORECASTS UNCERTAINTY DECISION ANALYSIS stochastic dynamic programming

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