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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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The use of stochastic dynamic programming in optimal landscape reconstruction for metapopulations

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ECOLOGICAL APPLICATIONS 2003年第2期13卷 543-555页

作者： Westphal, MI Pickett, M Getz, WM Possingham, HP Univ Queensland Ctr Ecol Dept Zool & Entomol St Lucia Qld 4072 Australia Univ Calif Berkeley Dept Environm Sci Policy & Management Berkeley CA 94720 USA Conservat Council S Australia Adelaide SA Australia Univ Queensland Dept Math St Lucia Qld 4067 Australia

A decision theory framework can be a powerful technique to derive optimal management decisions for endangered species. We built a spatially realistic stochastic metapopulation model for the Mount Lofty Ranges Southern Emu-wren (Stipiturus malachurus intermedius), a critically endangered Australian bird. Using diserete-time Markov,chains to describe the dynamics of a metapopulation and stochastic dynamic programming (SDP) to find optimal solutions, we evaluated the following different management decisions: enlarging existing patches, linking patches via corridors, and creating a new patch. This is the first application of SDP to optimal landscape reconstruction and one of the few times that landscape reconstruction dynamics have been integrated with population dynamics. SDP is a powerful tool that has advantages over standard Monte Carlo simulation methods because it can give the exact optimal strategy for every landscape configuration (combination of patch areas and presence of corridors) and pattern of metapopulation occupancy, as well as a trajectory of strategies. It is useful when a sequence of management actions can be performed over a given time horizon, as is the case for many endangered species recovery programs, where only fixed amounts of resources are available in each time step. However, it is generally limited by computational constraints to rather small networks of patches. The model shows that optimal metapopulation, management decisions depend greatly on the current state of the metapopulation,. and there is no strategy that is universally the best. The extinction probability over 30 yr for the optimal state-dependent management actions is 50-80% better than no management, whereas the best fixed state-independent sets of strategies are only 30% better than no management. This highlights the advantages of using a decision theory tool to investigate conservation strategies for metapopulations. It is clear from these results that the sequence of managem

关键词： Australia conservation decision theory metapopulation optimal landscape reconstruction Southern Emu-wren Stipiturus malachurus intermedius stochastic dynamic programming threatened species

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NONLINEAR OPTIMAL CONTROL OF A SEQUENTIAL INSPECTION OPERATION

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IFAC Proceedings Volumes 2007年第12期40卷 804-809页

作者： M. Pachter P.R. Chandler D. Swaroop AFIT/ENG 2950 Hobson Way Bldg. 640Wright-Patterson AFB OH 45433-7765 AFRL/VACA 2210 8th Street WPAFB OH 45433-7531

A simplified inspection scenario is considered where a Micro Air Vehicle with limited endurance is tasked with search and classification in a multi-target environment and where false, that is, clutter, targets are present. The sequential inspection operation, which includes a human operator for classification, is modelled, and a nonlinear discrete-time stochastic control problem is formulated. An analytic, closed-form, optimal control law is derived.

关键词： Nonlinear Optimal Control Sequential Inspection stochastic dynamic programming

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Optimal Portfolio Management in a CIR Framework

Optimal Portfolio Management in a CIR Framework

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第三届IEEE无线通讯、网络技术暨移动计算国际会议

作者： Shuping Wan College of Information Technology Jiangxi University of Finance and Economic Nanchang 330013P.R. China

The optimal portfolio problem for a bank account, single risky stock and a rolling horizon bond is developed. The stochastic short-term interest rate with the Cox-Ingersoll-Ross (CIR) dynamics affects the prices of the stock and rolling horizon bond. The investment objective is maximizing expected CRRA utility of terminal wealth. The problem has been solved by the stochastic dynamic programming principle and the completion of squares technique. The closed-form optimal trading strategy is obtained. A numerical example illustrating the results is presented.

关键词： portfolio rolling horizon bond Riccati equation stochastic dynamic programming

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Optimal capacity planning in stochastic loss networks with time-varying workloads 07

Optimal capacity planning in stochastic loss networks with t...

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Proceedings of the 2007 ACM SIGMETRICS international conference on Measurement and modeling of computer systems

作者： Sandeep Bhadra Yingdong Lu Mark S. Squillante University of Texas IBM Thomas J. Watson Research Center

ISBN: (纸本)9781595936394

We consider a capacity planning optimization problem in a general theoretical framework that extends the classical Erlang loss modeland related stochastic loss networks to support time-varying workloads. The time horizon consists of a sequence of coarse time intervals, each of which involves a stochastic loss network under a fixed multi-class workload that can change in a general manner from one interval to the next. The optimization problem consists of determining the capacities for each time interval that maximize a utility function over the entire time horizon, finite or infinite, where rewards gained from servicing customers are offset by penalties associated with deploying capacities in an interval and with changing capacities among intervals. We derive a state-dependent optimal policy within the context of a particular limiting regime of the optimization problem, and we prove this solution to be a symptotically optimal. Then, under fairly mild conditions, we prove that a similar structural property holds for the optimal solution of the original stochastic optimization problem, and we show how the optimal capacities comprising this solution can be efficiently computed.

关键词： stochastic dynamic programming erlang loss formula time-varying workloads stochastic loss networks asymptotic optimality erlang fixed-point approximation capacity planning

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Pricing American-style derivatives with European call options

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MANAGEMENT SCIENCE 2006年第1期52卷 95-110页

作者： Laprise, SB Fu, MC Marcus, SI Lim, AEB Zhang, HJ Adv Informat Technol BAE Syst Arlington VA 22203 USA Univ Maryland Robert H Smith Sch Business College Pk MD 20742 USA Univ Maryland Dept Elect & Comp Engn College Pk MD 20742 USA Univ Calif Berkeley Dept Ind Engn & Operat Res Berkeley CA 94720 USA

We present a new approach to pricing American-style derivatives that is applicable to any Markovian setting (i.e., not limited to geometric Brownian motion) for which European call-option prices are readily available. By approximating the value function with an appropriately chosen interpolation function, the pricing of an American-style derivative with arbitrary payoff function is converted to the pricing of a portfolio of European call options, leading to analytical expressions for those cases where analytical European call prices are available (e.g., the Merton jump-diffusion process). Furthermore, in many settings, the approach yields upper and lower analytical bounds that provably converge to the true option price. We provide computational results to illustrate the convergence and accuracy of the resulting estimators.

关键词： American-style derivatives American options European options call options early exercise stochastic dynamic programming

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On the existence of stationary optimal policies for partially observed MDPs under the long-run average cost criterion

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SYSTEMS & CONTROL LETTERS 2006年第2期55卷 165-173页

作者： Hsu, SP Chuang, DM Arapostathis, A Univ Texas Austin TX 78712 USA Natl Chi Nan Univ Puli 545 Nantou Taiwan

This paper studies the problem of the existence of stationary optimal policies for finite state controlled Markov chains, with compact action space and imperfect observations, under the long-run average cost criterion. It presents sufficient conditions for existence of solutions to the associated dynamic programming equation, that strengthen past results. There is a detailed discussion comparing the different assumptions commonly found in the literature. (c) 2005 Elsevier B.V. All rights reserved.

关键词： Markov decision processes optimal control stochastic dynamic programming imperfect information

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A qualitative approach to Markovian equilibrium on optimal growth under uncertainty

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JOURNAL OF dynamicAL AND CONTROL SYSTEMS 2006年第4期12卷 451-464页

作者： Carpio, L. G. T. Univ Fed Rio de Janeiro COPPE Energy Planning Program BR-21945 Rio De Janeiro Brazil

This paper develops a discretized version of a stochastic model of the economic growth and studies its convergence and stability properties. A nonlinear model of the economic growth, which involves the production, technology stock, and their rates as the main variables, is considered. We analyze the case where the production function does not satisfy the Inada conditions and we show that, in this case, a sufficient condition for the existence of a unique steady state is that the marginal utility function should possess a horizontal and vertical asymptotic elasticity.

关键词： natural resources optimal growth stochastic dynamic programming asymptotic stability

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Flexible supply policy with options and capacity constraints

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OPERATIONS RESEARCH LETTERS 2006年第5期34卷 508-516页

作者： Xu, Ningxiong Cornell Univ Sch Civil & Environm Engn Ithaca NY 14853 USA

This paper considers a class of multi-period flexible supply policies with options and capacity constraints. The main results are to characterize the optimal ordering and purchasing options policy and the minimum expected cost in a period and thereafter under the assumptions about the options and ordering quantities. (c) 2005 Elsevier B.V. All rights reserved.

关键词： inventory options capacity constraints additive function stochastic dynamic programming

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Spinning plates and squad systems: Policies for bi-directional restless bandits

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ADVANCES IN APPLIED PROBABILITY 2006年第1期38卷 95-115页

作者： Glazebrook, KD Kirkbride, C Ruiz-Hernandez, D Univ Lancaster Dept Math & Stat Lancaster LA1 4YF England Univ Lancaster Dept Management Sci Lancaster LA1 4YF England Univ Pompeu Fabra Dept Econ & Business E-08005 Barcelona Spain

This paper concerns two families of Markov decision problem that fall within the family of (bi-directional) restless bandits, an intractable class of decision processes introduced by Whittle. The spinning plates problem concerns the optimal management of a portfolio of reward-generating assets whose yields grow with investment but otherwise tend to decline. In the model of asset exploitation called the squad system, the yield from an asset tends to decline when it is used but will recover when the asset is at rest. In all cases, simply stated conditions are given that guarantee indexability of the problem, together with conditions necessary and sufficient for its strict indexability. The index heuristics for asset activation that emerge from the analysis are assessed numerically and found to perform very strongly.

关键词： index policy Lagrangian method Markov decision problem restless bandit stochastic dynamic programming

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