The purpose of the present work is to examine the financial problem of finding the reservation purchase price of a European call option written on a risky security when there is proportional transaction costs in the m...
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The purpose of the present work is to examine the financial problem of finding the reservation purchase price of a European call option written on a risky security when there is proportional transaction costs in the market. Existing papers within this area have all simplified the analysis by considering only one risky security and assumed exponential utility functions. The goal of the present paper is to suggest an approach to compute the reservation price of an option in an economy with more than one risky security and where trade involves transaction costs. Furthermore, the new approach enables us to investigate to what extent the above mentioned simplifications affect the reservation prices. We consider an economy with a riskless security, two risky securities, and agents' with HARA utility functions. We suggest an approach to compute reservation prices using convex optimization. Unfortunately, the proposed optimization models become large in terms of the number constraints and variables. However, using a newly developed interior-point algorithm, we manage to solve problems of an interesting size. The major findings are: (i) the investor's reservation purchase price of a European call option is almost insensitive to the functional form of the utility function, but sensitive (only slightly) to the initial level of absolute risk aversion, and (ii) the presence of diversification opportunities does not affect the reservation price in any unique way. (C) 1999 Elsevier Science B.V. and IMACS. All rights reserved.
This paper considers the problem of configuring a printed circuit board (PCB) assembly line experiencing uncertainty in demand and capacity. The PCB assembly process involves a single line of automatic placement machi...
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This paper considers the problem of configuring a printed circuit board (PCB) assembly line experiencing uncertainty in demand and capacity. The PCB assembly process involves a single line of automatic placement machines, a variety of board types, and a number of component types. The line is set up only once, at the beginning of a production cycle, to eliminate setups between board types. Using this strategy, the line therefore can assemble all different types of PCBs without feeder changes. The problem then becomes to partition component types to the different machines in the hope of processing all boards quickly with a good workload balance. In this paper, the board demands and machine breakdowns are random but follow some probability distribution, which can be predicted from past observations of the system. We formulate this problem as a stochastic mixed-integer programming formulation with the objective of minimizing the expected makespan for assembling all PCBs during a production cycle. The results obtained indicate significant improvement over the existing methods. We hope that this research will provide more PCB assembly facilities with models and techniques to hedge against variable forecasts and capacity plans
We introduce stochastic mathematical programs with equilibrium constraints (SMPEC), which generalize MPEC models by explicitly incorporating possible uncertainties in the problem data to obtain robust solutions to hie...
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We introduce stochastic mathematical programs with equilibrium constraints (SMPEC), which generalize MPEC models by explicitly incorporating possible uncertainties in the problem data to obtain robust solutions to hierarchical problems. For this problem, we establish results on the existence of solutions, and on the convexity and directional differentiability of the implicit upper-level objective function, both for continuously and discretely distributed probability distributions. In so doing, we establish links between SMPEC models and two-stage stochastic programs with recourse. We also discuss basic parallel iterative algorithms for discretely distributed SMPEC problems. (C) 1999 Elsevier Science B.V. All rights reserved.
We develop a scalable parallel implementation of the classical Benders decomposition algorithm for two-stage stochastic linear programs. Using a primal-dual, path-following algorithm for solving the scenario subproble...
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We develop a scalable parallel implementation of the classical Benders decomposition algorithm for two-stage stochastic linear programs. Using a primal-dual, path-following algorithm for solving the scenario subproblems we develop a parallel implementation that alleviates the difficulties of load balancing. Furthermore, the dual and primal step calculations can be implemented using a data-parallel programming paradigm. With this approach the code effectively utilizes both the multiple, independent processors and the vector units of the target architecture, the Connection Machine CM-5. The, usually limiting, master program is solved very efficiently using the interior point code LoQo on the front-end workstation. The implementation scales almost perfectly with problem and machine size. Extensive computational testing is reported with several large problems with up to 2 million constraints and 13.8 million variables.
This paper describes an advanced bottom-up approach for modelling the energy-environment sector to study greenhouse gas abatement. Three new features are described that give significant new capabilities to this class ...
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This paper describes an advanced bottom-up approach for modelling the energy-environment sector to study greenhouse gas abatement. Three new features are described that give significant new capabilities to this class of models. These are: endogenization of end-use demands, which allows computation of partial equilibria in energy markets;modelling future uncertainties using multi-stage stochastic programming;and combining several bottom-up models as a multi-region model to explore issues of cooperation and burden-sharing. Each of these new features is illustrated by results taken from large-scale extended MARKAL models of Quebec and Ontario. The focus of the paper is on the nature of issues that can be addressed by this methodology;rather than on specific conclusions drawn from the discussed examples. We believe that a very promising avenue of research lies in exploring the role of multiple advanced bottom-up models in the integrated assessment of climate change.
In recent years management of customer requirements has been the foremost concern of most manufacturers. In this paper, we consider a single-period problem in which the manufacturer faces stochastic demand and individ...
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In recent years management of customer requirements has been the foremost concern of most manufacturers. In this paper, we consider a single-period problem in which the manufacturer faces stochastic demand and individual service level constraints from multiple customers. We present a formulation for the problem that utilizes the structure of the underlying allocation problem and provide an algorithm that generates the optimal procurement quantity under the optimal random allocation policy. For a special case when there are two identical customers and their demand is jointly uniform, we derive an analytical expression for the optimal procurement quantity. (C) 1999 Elsevier Science B.V. All rights reserved.
For a company that produces a product in a range of sizes, it is sometimes possible to meet demand for a smaller size by substituting a larger size. In this paper, we give an integer linear programming model that addr...
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For a company that produces a product in a range of sizes, it is sometimes possible to meet demand for a smaller size by substituting a larger size. In this paper, we give an integer linear programming model that addresses this issue. Various characteristics of the optimal policy are given. These properties are exploited when the formulation is extended to the multi-period stochastic demand case. This application was motivated by our experience with a company that manufactures a range of multiple-piece blind fasteners where savings in setup cost can be made using long-grip fasteners to meet the demand for short-grip fasteners.
Introducing probabilistic constraints leads in general to nonconvex, nonsmooth or even discontinuous optimization models. In this paper, necessary and sufficient conditions for metric regularity of(several joint) prob...
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Introducing probabilistic constraints leads in general to nonconvex, nonsmooth or even discontinuous optimization models. In this paper, necessary and sufficient conditions for metric regularity of(several joint) probabilistic constraints are derived using recent results from nonsmooth analysis. The conditions apply to fairly general constraints and extend earlier work in this direction. Further. a verifiable sufficient condition for quadratic growth of the objective function in a more specific convex stochastic program is indicated and applied in order to obtain a new result on quantitative stability of solution sets when the underlying probability distribution is subjected to perturbations. This is used to derive bounds for the deviation of solution sets when the probability measure is replaced by empirical estimates.
stochastic multi-stage linear programs are rarely used in practical applications due to their size and complexity. Using a general matrix to aggregate the constraints of the deterministic equivalent yields a lower bou...
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stochastic multi-stage linear programs are rarely used in practical applications due to their size and complexity. Using a general matrix to aggregate the constraints of the deterministic equivalent yields a lower bound. A similar aggregation in the dual space provides an upper bound on the optimal value of the given stochastic program. Jensen's inequality and other approximations based on aggregation are a special case of the suggested approach. The lower and upper bounds are tightened by updating the aggregating weights. (C) 1999 Elsevier Science B.V. All rights reserved.
作者：
Dayan, PMIT
Dept Brain & Cognit Sci Cambridge MA 02139 USA
Many recent analysis-by-synthesis density estimation models of cortical learning and processing have made the crucial simplifying assumption that units within a single layer are mutually independent given the states o...
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Many recent analysis-by-synthesis density estimation models of cortical learning and processing have made the crucial simplifying assumption that units within a single layer are mutually independent given the states of units in the layer below or the layer above. In this article, we suggest using either a Markov random field or an alternative stochastic sampling architecture to capture explicitly particular forms of dependence within each layer. We develop the architectures in the context of real and binary Helmholtz machines. Recurrent sampling can be used to capture correlations within layers in the generative or the recognition models, and we also show how these can be combined.
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