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The optimal dynamic allocation of conservation funds under financial uncertainty

ECOLOGICAL ECONOMICS 2007年第2-3期61卷 255-266页

作者： Drechsler, Martin Waetzold, Frank UFZ Helmholtz Ctr Environm Res Dept Ecol Modelling D-04318 Leipzig Germany UFZ Helmholtz Ctr Environm Res Dept Econ D-04318 Leipzig Germany

This paper analyses a situation where the survival of an endangered species depends on certain types of conservation measures being carried out regularly, yet there is financial uncertainty in the future periodical availability of a budget to finance the conservation measures. One option to insure against future budget uncertainty is to save money. To maximise the long-term survival of the endangered species, it has to be decided in each period whether to spend the available money now or to allocate it to future use. The paper provides an ecological-economic model for this stochastic dynamic optimisation problem. The findings include that the available money should be allocated as evenly as possible among periods, which may require some precautionary saving in early periods to take uncertainty into account. Under certain conditions, however, increasing uncertainty may at least temporarily increase the optimal payment. Among other parameters, the amount of precautionary actions depends on the magnitude of natural variation in the species population. (c) 2006 Elsevier B.V. All rights reserved.

关键词： biodiversity conservation ecological-economic modelling stochastic dynamic programming uncertainty precautionary saving

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Mean-variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns

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INSURANCE MATHEMATICS & ECONOMICS 2015年 61卷 99-109页

作者： Guan, Guohui Liang, Zongxia Tsinghua Univ Dept Math Sci Beijing 100084 Peoples R China

This paper studies the optimization problem of DC pension plan under mean-variance criterion. The financial market consists of cash, bond and stock. Similar to Guan and Liang (2014), we assume that the instantaneous interest rate is an affine process including the Cox-Ingersoll-Ross (CIR) model and Vasicek model. However, we assume that the expected return of the stock follows a completely different mean-reverting process, which can well display the bear and bull features of the market, and the market price of the stock index is the Ornstein-Uhlenbeck process. The pension manager thus has to undertake the risks of interest rate and market price of stock index. Besides, a special stochastic contribution rate is formulated. The goal of the pension manager is to maximize the expected terminal value and minimize the variance of terminal value. We will use the technique developed by Guan and Liang (2014) to tackle this problem and derive the closed-forms of efficient frontier and strategies. Numerical analysis is given in the end of this paper to show the economic behavior of the efficient frontier and strategies. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Defined contribution pension plan stochastic interest rate Mean-reverting returns stochastic market price of risk Mean-variance efficiency stochastic dynamic programming

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A recursive Riccati interior-point method for chance-constrained stochastic model predictive control

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SICE JOURNAL OF CONTROL MEASUREMENT AND SYSTEM INTEGRATION 2023年第1期16卷 273-285页

作者： Zhang, Jingyu Ohtsuka, Toshiyuki Kyoto Univ Grad Sch Informat Dept Syst Sci Kyoto Japan

This study covers the model predictive control of linear discrete-time systems subject to stochastic additive disturbances and state chance constraints. The stochastic optimal control problem is reformulated in a dynamic programming fashion to obtain a closed-loop performance and is solved using the interior-point method combined with a Riccati-based approach. The proposed method eliminates active sets in conventional explicit model predictive control and does not suffer from the curse of dimensionality because it finds the value function and feedback policy only for a given initial state using the interior-point method. Moreover, the proposed method is proven to converge globally to the optimal solution Q-superlinearly. The numerical experiment shows that the proposed method achieves a less conservative performance with a low computational complexity compared to existing methods.

关键词： stochastic systems chance constraint model predictive control stochastic dynamic programming closed-loop policy

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41 Counterexamples to property (B) of the discrete time bomber problem

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ANNALS OF OPERATIONS RESEARCH 2017年第1-2期248卷 579-588页

作者： Kamihigashi, Takashi Kobe Univ Res Inst Econ & Business Adm RIEB Nada Ku Kobe Hyogo 6578501 Japan

The discrete time "bomber problem" has been one of the longest standing open problems in operations research. In particular, the validity of one of the natural monotonicity conjectures-known as property (B)-has been an unresolved issue since 1968. In this paper we report 41 counterexamples to property (B) of this problem. We have found them by computing the exact solutions for nearly one million pairs of parameter values utilizing the GNU multiple precision arithmetic library. All our counterexamples can readily be verified using a simple Mathematica program included in this paper.

关键词： The discrete time bomber problem Error-free methods GNU multiple precision (GMP) arithmetic library stochastic dynamic programming

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PHASE TRANSITION IN A SEQUENTIAL ASSIGNMENT PROBLEM ON GRAPHS

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ANNALS OF APPLIED PROBABILITY 2017年第4期27卷 2098-2129页

作者： Jarai, Antal A. Univ Bath Dept Math Sci Bath BA1 7AY Avon England

We study the following game on a finite graph G = (V,E). Each edge e is an element of E starts with an integer value n(e) >= 0, and we write n = Sigma eE n(e). At time t, 1 infinity, the expected reward under the ... 详细信息

We study the following game on a finite graph G = (V,E). Each edge e is an element of E starts with an integer value n(e) >= 0, and we write n = Sigma eE n(e). At time t, 1 <= t <= n, a uniformly random vertex v is an element of V is generated, and one of the edges f incident with v must be selected. The value of f is then decreased by 1. There is a unit final reward if the configuration (0,...,0) is reached. Our main result is that there is a phase transition: as n -> infinity, the expected reward under the optimal policy approaches a constant c(G) > 0 when (n(e)/n : e is an element of E) converges to a point in the interior of a certain convex set R-G, and goes to 0 exponentially when (n(e)/n : e is an element of E) is bounded away from R-G. We also obtain estimates in the near-critical region, that is when (ne/n : e. E) lies close to partial derivative RG. We supply quantitative error bounds in our arguments.

关键词： Phase transition critical phenomenon stochastic sequential assignment Markov decision process stochastic dynamic programming discrete stochastic optimal control

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Explicit Solution for Constrained Optimal Execution Problem with General Correlated Market Depth

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Journal of the Operations Research Society of China 2018年第1期6卷 159-174页

作者： Wei-Ping Wu Jian-Jun Gao School of Information Management and Engineering Shanghai University of Finance and EconomicsShanghai 200433China Department of Automation Shanghai Jiao Tong UniversityShanghai 200241China

This work studies the constrained optimal execution problem with a random market depth in the limit order *** from the real trading activities,our execution model considers the execution bounds and allows the random market depth to be statistically correlated in different ***,it is difficult to achieve the analytical solution for this class of constrained dynamic decision *** to the special structure of this model,by applying the proposed state separation theorem and dynamic programming,we successfully obtain the analytical execution *** revealed policy is of feedback *** are provided to illustrate our solution *** results demonstrate the advantages of our model comparing with the classical execution policy.

关键词： Optimal execution problem Random market depth Limit order book stochastic dynamic programming

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State dependent behavior and the Marginal Value Theorem

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BEHAVIORAL ECOLOGY 2001年第1期12卷 71-83页

作者： Nonacs, P Univ Calif Los Angeles Dept Organism Biol Ecol & Evolut Los Angeles CA 90095 USA

The Marginal Value Theorem (MVT) is the dominant paradigm in predicting patch use and numerous tests support its qualitative predictions. Quantitative tests under complex foraging situations could be expected to be more variable in their support because the MVT assumes behavior maximizes only net energy-intake rate. However across a survey of 26 studies, foragers rather consistently "erred" in staying too long in patches. Such a consistent direction to the errors suggests that the simplifying assumptions of the MVT introduce a systematic bias rather than just imprecision. Therefore, I simulated patch use as a state-dependent response to physiological state, travel cost, predation risk, prey densities, and fitness currencies other than net-rate maximization (e.g., maximizing survival, reproductive investment, or mating opportunities). State-dependent behavior consistently results in longer patch residence times than predicted by the MVT or another foraging model, the minimize mu /g rule, and these rules fail to closely approximate the best behavioral strategy over a wide range of conditions. Because patch residence times increase with state-dependent behavior, this also predicts mass regulation below maximum energy capacities without direct mass-specific costs. Finally, qualitative behavioral predictions from the MVT about giving-up densities in patches and the effects of travel costs are often inconsistent with state-dependent behavior. Thus in order to accurately predict patch exploitation patterns, the model highlights the need to: (1) consider predator behavior (sit-and-wait versus actively foraging);(2) identify activities that can occur simultaneously to foraging (i.e., mate search or parental care);and (3) specify the range of nutritional states likely in foraging animals. Future predictive models of patch use should explicitly consider these parameters.

关键词： marginal value theorem predation risk foraging patch use stochastic dynamic programming state-dependent behavior

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stochastic optimal switching model for migrating population dynamics

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JOURNAL OF BIOLOGICAL dynamicS 2019年第1期13卷 706-732页

作者： Yoshioka, Hidekazu Tanaka, Tomomi Aranishi, Futoshi Izumi, Tomoki Fujihara, Masayuki Shimane Univ Grad Sch Nat Sci & Technol Matsue Shimane Japan Shimane Univ Fisheries Ecosyst Project Ctr Matsue Shimane Japan Ehime Univ Grad Sch Agr Matsuyama Ehime Japan Kyoto Univ Grad Sch Agr Kyoto Japan

An optimal switching control formalism combined with the stochastic dynamic programming is, for the first time, applied to modelling life cycle of migrating population dynamics with non-overlapping generations. The migration behaviour between habitats is efficiently described as impulsive switching based on stochastic differential equations, which is a new standpoint for modelling the biological phenomenon. The population dynamics is assumed to occur so that the reproductive success is maximized under an expectation. Finding the optimal migration strategy ultimately reduces to solving an optimality equation of the quasi-variational type. We show an effective linkage between our optimality equation and the basic reproduction number. Our model is applied to numerical computation of optimal migration strategy and basic reproduction number of an amphidromous fish Plecoglossus altivelis altivelis in Japan as a target species.

关键词： stochastic dynamic programming fish migration Hamilton-Jacobi-Bellman equation basic reproduction number Plecoglossus altivelis altivelis

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Inventory Management under Storage and Order Restrictions

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PRODUCTION AND OPERATIONS MANAGEMENT 2020年第1期29卷 101-117页

作者： Sharma, Shrutivandana Abouee-Mehrizi, Hossein Sartor, Giorgio Singapore Univ Technol & Design Engn Syst & Design 8 Somapah Rd Singapore 487372 Singapore Univ Waterloo Dept Management Sci 200 Univ Ave W Waterloo ON N2L 3G1 Canada SINTEF Digital Dept Math & Cybernet Forskningsveien 1 N-0373 Oslo Norway

Inventory management in most practical settings faces challenges due to various restrictions on storage and replenishment of products. These restrictions may be posed by budget availability, different production/supply schedules for different products, and limited storage space shared by a number of products-very common in retail, food, and the pharmaceutical industry. Motivated by this, we investigate in this study how simultaneous restrictions on shared storage capacity and product-specific order capacities impact optimal replenishments in a multi-product system. We formulate the inventory replenishment problem as a multi-period stochastic dynamic program, where products face stochastic demand with general distributions and excess demand is lost or fulfilled by emergency orders. We first fully characterize the optimal replenishment policy for two-product systems, and provide a methodology to compute optimal replenishment quantities, which can be described as a dynamic priority-based replenishment rule. Our results show that for each product, the optimal replenishment priority as well as quantity depends on the inventory levels of both products and all available capacities. More interestingly, the results show that capacity restrictions can flip the stocking priorities of products. Based on the optimal policy for two-product systems, we develop a heuristic for multi-product systems whose complexity scales linearly with the number of products. Under moderate storage capacities, our heuristic significantly outperforms the naive heuristics that ignore dynamic priority assignment, and closely captures the benefits of the optimal policy for systems with large number of products.

关键词： inventory management storage capacity order capacity optimal replenishment stochastic dynamic programming

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Foraging in a tidally structured environment by red knots (Calidris canutus):: Ideal, but not free

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ECOLOGY 2006年第5期87卷 1189-1202页

作者： van Gils, Jan A. Spaans, Bernard Dekinga, Anne Piersma, Theunis Royal Netherlands Inst Sea Res Dept Marine Ecol & Evolut NL-1790 AB Den Burg Netherlands Univ Groningen CEES Anim Ecol Grp NL-9750 AA Haren Netherlands

Besides the "normal" challenge of obtaining adequate intake rates in a patchy and dangerous world, shorebirds foraging in intertidal habitats face additional environmental hurdles. The tide forces them to commute between a roosting site and feeding grounds, twice a day. Moreover, because intertidal food patches are not all available at the same time, shorebirds should follow itineraries along the best patches available at a given time. Finally, shorebirds need additional energy stores in order to survive unpredictable periods of bad weather, during which food patches are covered by extreme tides, In order to model such tide-specific decisions, we applied stochastic dynamic programming in a spatially explicit context. Two assumptions were varied, leading to four models. First, birds had either perfect (ideal) or no (non-ideal) information about the intake rate at each site. Second, traveling between sites was either for free or incurred time and energy costs (non-free). Predictions were generated for three aspects of foraging: area use, foraging routines, and energy stores. In general, non-ideal foragers should feed most intensely and should maintain low energy stores. If traveling for such birds is free, they should feed at a random site;otherwise, they should feed close to their roost. Ideal foragers should concentrate their feeding around low tide (especially when free) and should maintain larger energy stores (especially when non-free). If traveling for such birds is free, they should feed at the site offering the highest intake rate;otherwise, they should trade off travel costs and intake rate. Models were parameterized, for Red Knots (Calidris canutus) living in the Dutch Wadden Sea in late summer, an area for which detailed, spatially explicit data on prey densities and tidal heights are available. Observations of radio-marked knots (area use) and unmarked knots (foraging routines, energy stores) showed the closest match with the ideal/non-free model. We concl

关键词： Calidris canutus daily routine foraging patch use Red Knot state-dependent decisions stochastic dynamic programming tidal regime Wadden Sea

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