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Pricing American-style derivatives with European call options

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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Finite horizon minimax optimal control of nonlinear continuous time systems with stochastic uncertainty

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dynamicS AND CONTROL 2000年第1期10卷 63-86页

作者： Ugrinovskii, VA Petersen, IR Australian Def Force Acad Sch Elect Engn Canberra ACT 2600 Australia

This paper develops a general continuous-time stochastic framework for robustness analysis and robust control synthesis. We consider a stochastic minimax optimization problem for general stochastic uncertain systems. A general method is presented for converting problems of performance analysis or controller synthesis into unconstrained optimization problems.

关键词： stochastic systems stochastic control robust control robust performance minimax stochastic optimization stochastic dynamic programming

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On the value and price-responsiveness of ramp-constrained storage

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ENERGY CONVERSION AND MANAGEMENT 2013年 76卷 472-482页

作者： Faghih, Ali Roozbehani, Mardavij Dahleh, Munther A. MIT Elect Engn & Comp Sci EECS Dept Cambridge MA 02139 USA MIT Lab Informat & Decis Syst Cambridge MA 02139 USA

The primary concerns of this paper are twofold: understanding the value of storage in the presence of ramp constraints and exogenous energy prices, and understanding the implications of the associated optimal storage management policy for qualitative and quantitative characteristics of storage response to real-time prices. The optimal policy, along with the associated finite-horizon time-averaged value of storage, are analytically characterized in this paper. An analytical upper bound on the infinite-horizon time-averaged value of storage is also derived. This bound is valid for any achievable realization of prices when the support of the distribution is fixed, and highlights the dependence of the value of storage on ramp constraints and storage capacity. It is shown that while the value of storage is a non-decreasing function of price volatility, due to the finite ramp rate, the value of storage saturates quickly as the capacity increases, regardless of volatility. To study the implications of the optimal policy, computational experiments are presented that suggest optimal utilization of storage can, in expectation, induce a considerable amount of price elasticity near the average price. Then, a computational framework is presented for characterization of the behavior of storage as a function of price and the state of charge, which illustrates a steep buy/sell phase transition in the price-state plane. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Ramp-constrained energy storage stochastic dynamic programming Control systems

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MYOPIC POLICIES FOR NON-PREEMPTIVE SCHEDULING OF JOBS WITH DECAYING VALUE

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PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES 2018年第1期32卷 1-36页

作者： Master, Neal Chan, Carri W. Bambos, Nicholas Stanford Univ Dept Elect Engn Stanford CA 94305 USA Columbia Business Sch Decis Risk & Operat New York NY USA Stanford Univ Dept Management Sci & Engn Stanford CA 94305 USA

In many scheduling applications, minimizing delays is of high importance. One adverse effect of such delays is that the reward for completion of a job may decay over time. Indeed in healthcare settings, delays in access to care can result in worse outcomes, such as an increase in mortality risk. Motivated by managing hospital operations in disaster scenarios, as well as other applications in perishable inventory control and information services, we consider non-preemptive scheduling of jobs whose internal value decays over time. Because solving for the optimal scheduling policy is computationally intractable, we focus our attention on the performance of three intuitive heuristics: (1) a policy which maximizes the expected immediate reward, (2) a policy which maximizes the expected immediate reward rate, and (3) a policy which prioritizes jobs with imminent deadlines. We provide performance guarantees for all three policies and show that many of these performance bounds are tight. In addition, we provide numerical experiments and simulations to compare how the policies perforin in a variety of scenarios. Our theoretical and numerical results allow us to establish rules-of-thumb for applying these heuristics in a variety of situations, including patient scheduling scenarios.

关键词： operations research stochastic dynamic programming stochastic modelling

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Operation Policies through dynamic programming and Genetic Algorithms, for a Reservoir with Irrigation and Water Supply Uses

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WATER RESOURCES MANAGEMENT 2021年第5期35卷 1573-1586页

作者： Mendoza Ramirez, Rosalva Arganis Juarez, Maritza Liliana Dominguez Mora, Ramon Padilla Morales, Luis Daniel Fuentes Mariles, Oscar Arturo Mendoza Resendiz, Alejandro Carrizosa Elizondo, Eliseo Carmona Paredes, Rafael Bernardo Univ Nacl Autonoma Mexico Inst Ingn Campus Morelia Morelia 58190 Michoacan Mexico Univ Nacl Autonoma Mexico Inst Ingn Ave Univ 3000 Mexico City 04510 DF Mexico

In this study, operation policies were obtained for a reservoir in Michoacan, Mexico, used for irrigation and domestic water supplies. The main purpose of these policies is to optimize the uses of the water, an increasingly scarce resource everywhere. Two optimization methodologies were used;stochastic dynamic programming, that provides release decisions for each stage, and genetic algorithms coupled with a reservoir operation simulation program, to achieve annual release curves. The operation of the reservoir was evaluated using historical inflow records. Monthly requirements for crop cycles, as well as the volumes of spills and deficits were examined. Both methodologies gave inverse relationships between deficits and spilled volumes. While both methodologies proved efficient in achieving the objectives, the results of the stochastic dynamic programming showed a better performance for this system.

关键词： stochastic dynamic programming Genetic algorithms Optimal management Cointzio reservoir

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Partial Equilibrium in Risk-Based Production Decisions

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NAVAL RESEARCH LOGISTICS 2012年第1期59卷 1-17页

作者： Kamrad, Bardia Siddique, Akhtar Ernst, Ricardo Georgetown Univ McDonough Sch Business Washington DC 20057 USA Off Comptroller Currency Enterprise Risk Anal Div Washington DC 20219 USA

Characteristically, a small subset of operational problems admit risk neutrality when contingent claims methodology were used in their analysis. That is, for the majority of manufacturing and production problems, operating cash flows are not directly linked to prices of traded assets. However, to the extent that correlations can be estimated, the methodology's applicability to a broader set of operational problems is supported. Our article addresses this issue with the objective of extending the use of contingent claims techniques to a larger set of operational problems. In broad terms, this objective entails a partial equilibrium approach to the problem of valuing uncertain cash flows. To this end, we assume risk aversion and cast our approach within Merton's intertemporal capital asset pricing model. In this context, we formulate a "generic" production valuation model that is framed as an exercise in stochastic optimal control. The model is versatile in its characterization and can easily be adapted to accommodate a wide-ranging set of risk-based operational problems where the underlying sources of uncertainty are not traded. To obtain results, the model is recast as a stochastic dynamic program to be solved numerically. The article addresses a number of fundamental issues in the analysis risk based decision problems in operations. First, in the approach provided, decisions are analyzed under a properly defined risk structure. Second, the process of analysis leads to suitably adjusted probability distributions through which, appropriately discounted expectations are derived. Third, through consolidating existing concepts into a standard and adaptable framework, we extend the applicability of contingent claims methodology to a broader set of operational problems. The approach is advantageous as it obviates the need for exogenously specifying utility functions or discount rates. (C) 2011 Wiley Periodicals, Inc. Naval Research Logistics 59: 1-17, 2012

关键词： contingent claims analysis in production operations control theory Merton's intertemporal capital asset pricing model stochastic dynamic programming risk management in operations

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Reducing passenger waiting time in oversaturated metro lines with passenger flow control policy

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2023年 117卷

作者： Liang, Jinpeng Zang, Guangzhi Liu, Haitao Zheng, Jianfeng Gao, Ziyou Dalian Maritime Univ Sch Transportat Engn Dalian Peoples R China China Acad Railway Sci Corp Ltd Inst Comp Technol Beijing Peoples R China Sichuan Univ Business Sch Chengdu Peoples R China Beijing Jiaotong Univ Sch Traff & Transportat Beijing Peoples R China

Oversaturation during peak hours brings about severe challenges for metro operations management in megacities. It can deteriorate passengers' service level experience and increase the safety risk at congested platforms. This paper focuses on designing an online passenger flow control policy to manage passenger flow in each origin-destination (OD) pair so that the total passenger waiting time during the research horizon can be minimized. Suppose that the OD demand information reveals sequentially over time, we formulate the online passenger flow control problem as stochastic dynamic programming (DP). An efficient online adaptive policy is designed to guide the real-time flow control decisions at each stage. To evaluate the performance of our approach, we exploit the realistic transit data from the Beijing metro system to carry out a series of numerical experiments. The computational results show that our approach can significantly reduce the expected total passenger waiting time as well as alleviate metro station congestion compared with the first-come-first-serve (FCFS) policy. The benefits of our approach are obtained by exploiting the reusable nature of train capacity to transport more passengers during rush hours.(c) 2023 Elsevier Ltd. All rights reserved.

关键词： metro system oversaturation passenger flow control online algorithm stochastic dynamic programming

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Should environmental constraints be considered in linear programming based water value calculators?

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2020年第0期117卷 105662-000页

作者： Guisandez, Ignacio Ignacio Perez-Diaz, Juan Nowak, Wolfgang Haas, Jannik Univ Politecn Madrid Dept Hydraul Energy & Environm Engn E-28040 Madrid Spain Univ Stuttgart Dept Stochast Simulat & Safety Res Hydrosyst IWS D-70569 Stuttgart Germany

We evaluate the practical usefulness of incorporating maximum ramping rates and minimum environmental flows into a linear programming based water value calculator for hydropower plants that participate in the day-ahead electricity market. The methodology consists of three steps: first computing the water value once with and once without environmental constraints, then simulating the plant operations using each water value, and finally comparing the simulation profits. A set of nine representative hydropower plants formed by combinations of three real locations (in Colombia, Norway and Spain) and three turbine configurations (from one to three Francis units) are individually analyzed. Each plant is simulated in two synthetic 10-year long series subject to fifteen combinations of maximum ramping rates and minimum flows with the two above-mentioned water values, totaling 540 simulations. The results indicate that incorporating the analyzed environmental constraints into a linear programming based water value calculator can be significantly profitable only when the hydropower plants have only one or at most two turbines.

关键词： Maximum ramping rate Minimum environmental flow Linear programming Mixed integer linear programming stochastic dynamic programming

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Fully polynomial time (Sigma, Pi)-approximation schemes for continuous nonlinear newsvendor and continuous stochastic dynamic programs

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MATHEMATICAL programming 2022年第1-2期195卷 183-242页

作者： Halman, Nir Nannicini, Giacomo Bar Ilan Univ Ramat Gan Israel IBM TJ Watson Res Ctr IBM Quantum Yorktown Hts NY USA

We study the nonlinear newsvendor problem concerning goods of a non-discrete nature, and a class of stochastic dynamic programs with several application areas such as supply chain management and economics. The class is characterized by continuous state and action spaces, either convex or monotone cost functions that are accessed via value oracles, and affine transition functions. We establish that these problems cannot be approximated to any degree of either relative or additive error, regardless of the scheme used. To circumvent these hardness results, we generalize the concept of fully polynomial-time approximation scheme allowing arbitrarily small additive and multiplicative error at the same time, while requiring a polynomial running time in the input size and the error parameters. We develop approximation schemes of this type for the classes of problems mentioned above. In light of our hardness results, such approximation schemes are "best possible". A computational evaluation shows the promise of this approach.

关键词： Newsvendor problem stochastic inventory control Hardness of approximation Approximation algorithms stochastic dynamic programming K -approximation sets and functions

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Adaptive water infrastructure planning for nonstationary hydrology

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ADVANCES IN WATER RESOURCES 2018年 118卷 83-94页

作者： Hui, Rui Herman, Jonathan Lund, Jay Madani, Kaveh Univ Calif Davis Ctr Watershed Sci Davis CA 95616 USA Univ Calif Davis Dept Civil & Environm Engn Davis CA 95616 USA Imperial Coll London Ctr Environm Policy London SW7 2AZ England Stockholm Univ Dept Phys Geog Stockholm Sweden

The uncertainty of a changing climate raises challenges for water infrastructure planning and design. Not accounting for nonstationarity may result in under-designed structures that fail too frequently, or over-designed structures that are economically inefficient. This concern is magnified by uncertainty in the long-term frequency and magnitude of future extreme events. Planning strategies that allow adaptations over a structure's life could improve both reliability and economic efficiency. This study develops a method to inform adaptive water infrastructure planning with uncertain hydrologic and other forms of nonstationarity, applied to levee system planning. A stochastic dynamic programming model including a Markov process is developed for infrastructure planning with uncertain nonstationarity in flood frequency. Bayes' theorem is used to update peak flow probabilities conditioned on observed past peak flows and to update expected residual flood damages over time. A levee system planning problem with a numerical example from California illustrates the approach to derive optimal levee heights over time, and economic values of adapting to uncertain nonstationary flood risk. The projected range of probabilistic hydrology scenarios affects the optimal results, particularly in later planning stages as hydrology scenarios diverge with time. Adaptive planning strategies allowing more levee upgrades over time slightly lowers the overall cost and provides better flood protection than one-time construction under nonstationary hydrology for any climate in the example. Compared to a known future nonstationary hydrology, incorporating uncertain nonstationary climate results in higher levees being planned for observed severe hydrology scenarios in later stages. The overall present value cost with uncertain nonstationary climate depends on rates of change in peak flow distribution parameters in future hydrology scenarios.

关键词： Nonstationary hydrology Uncertain nonstationarity Water infrastructure planning stochastic dynamic programming Risk-based analysis

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