Stochastic Programming : Applications in Finance, Energy, Planning and Logistics.

By: Ziemba, William TContributor(s): Gassmann, Horand I | Ziemba, William TMaterial type: TextTextSeries: World Scientific Series in Finance SerPublisher: Singapore : World Scientific Publishing Co Pte Ltd, 2012Copyright date: ©2012Description: 1 online resource (549 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9789814407519Subject(s): Decision making | Mathematical optimization -- Industrial applications | Mathematical optimization | Stochastic processes -- Econometric models | Stochastic programming | UncertaintyGenre/Form: Electronic books.Additional physical formats: Print version:: Stochastic Programming : Applications in Finance, Energy, Planning and LogisticsDDC classification: 519.7 LOC classification: HB143.7 -- .S76 2013ebOnline resources: Click to View
Contents:
Intro -- Contents -- Acknowledgements -- List of Contributors -- Preface -- Books and Collections of Papers on Stochastic Programming -- 1. Introduction and Summary -- Part I. Papers in Finance -- 2. Longevity Risk Management for Individual Investors Woo Chang Kim, John M. Mulvey, Koray D. Simsek and Min Jeong Kim -- 1 Introduction -- 2 Model -- 3 Numerical results -- 3.1 First example: Retirement planning without longevity risk consideration -- 3.2 Second example: Impact of longevity risk to retirement planning -- 3.3 Third example: Longevity risks in pension benefits -- 4 Conclusions -- References -- 3. Optimal Stochastic Programming-Based Personal Financial Planning with Intermediate and Long-Term Goals Vittorio Moriggia, Giorgio Consigli and Gaetano Iaquinta -- 1 Introduction -- 2 The asset-liability management model -- 2.1 Individual wealth, consumption and investment targets -- 2.2 Random coefficients and scenarios -- 2.3 The optimization problem -- 3 Numerical implementation and case study -- 3.1 Decision tool modular structure -- 3.1.1 Individual policy statement -- 3.1.2 Scenario manager -- 3.1.3 Output -- 3.2 Case study -- 3.2.1 Optimal solutions -- 4 Conclusion -- References -- 4. Intertemporal Surplus Management with Jump Risks Mareen Benk -- 1 Introduction -- 2 An intertemporal surplus management model with jump risks - a three-fund theorem -- 3 Risk preference, and funding ratio -- 4 Conclusions -- Appendix I: Derivation of the asset specific risk factor of the first jump component -- Appendix II: Derivation of equation (16) -- Appendix III: Derivation of equation (17) -- References -- 5. Jump-Diffusion Risk-Sensitive Benchmarked Asset Management Mark Davis and Sebastien Lleo -- 1 Introduction -- 2 Analytical setting -- 2.1 Factor dynamics -- 2.2 Asset market dynamics -- 2.3 Benchmark modelling -- 2.4 Portfolio dynamics.
2.5 Investment constraints -- 2.6 Problem formulation -- 3 Dynamic programming and the value function -- 3.1 The risk-sensitive control problems under Ph -- 3.2 Properties of the value function -- 3.3 Main result -- 4 Existence of a classical (C1,2) solution under affine drift assumptions -- 5 Existence of a classical (C1,2) solution under standard control assumptions -- 6 Verification -- 6.1 The unique maximizer of the supremum (60) is the optimal control, i.e. h*(t,Xt) = h (t,Xt,D (t,Xt)) -- 6.2 Verification -- 7 Conclusion -- References -- 6. Dynamic Portfolio Optimization under Regime-Based Firm Strength Chanaka Edirisinghe and Xin Zhang -- 1 Introduction -- 2 DEA-based relative firm strength -- 2.1 Financial DEA model -- 2.2 Parameters of RFS -- 2.3 Correlation analysis -- 3 Modeling market regimes -- 3.1 Regime analysis (1971-2010) -- 3.2 Regime-based firm-RFS -- 4 Portfolio optimization under regime-based RFS -- 4.1 RFS-based stock selections -- 4.2 Decisions under regime-scenarios -- 4.3 Transactions cost model -- 4.4 Budget constraints -- 4.5 Risk-return framework -- 4.6 Two-period optimization model -- 5 Model application -- 5.1 RFS estimation and firm selections -- 5.2 Portfolio analysis -- 6 Conclusions -- Acknowledgement -- References -- 7. Options Portfolio Management as a Chance Constrained Problem Dmitry Golembiovsky and Anatoliy Abramov -- 1 Introduction -- 2 Model of options market -- 3 A scenario model for stochastic programming -- 4 The problem of option portfolio optimization -- 5 Solving the problem and some simulation results -- 6 Conclusions and future research -- References -- 8. Stochastic Models for Optimizing Immunization Strategies in Fixed-Income Security Portfolios under Some Sources of Uncertainty Larraitz Aranburu, Laureano F. Escudero, M. Araceli Garin and Gloria Perez -- 1 Introduction.
2 The deterministic LP optimization model -- 3 Two sources of uncertainty: interest rate and credit risk -- 4 Traditional two-stage stochastic optimization approach -- 5 Risk adverse models -- 5.1 Mean-risk immunization strategy -- 5.2 Value-at-Risk (VaR) strategy -- 5.3 Stochastic dominance strategy -- 6 Two-stage fixed-income security portfolio immunization based on the VaR strategy -- 7 A more accurate solution: a multistage stochastic scheme -- 7.1 Multistage maxmin immunization strategy -- 7.2 Multistage stochastic dominance strategy -- 7.3 Multistage VaR & stochastic dominance strategy -- 8 Case study -- 8.1 Deterministic LP model -- 8.2 Two-stage scheme -- 8.3 Two-stage stochastic model (DEM1) -- 8.4 Mean-risk immunization model (DEM-MR) -- 8.5 Two-stage maxmin immunization model (DEM2) -- 8.6 Two-stage VaR model (DEM3) -- 8.7 Multistage scheme -- 8.8 Multistage maxmin immunization model (DEM4) -- 8.9 Multistage stochastic dominance model (DEM5) -- 8.10 Multistage VaR & stochastic dominance model (DEM6) -- 9 Models comparison and conclusions -- References -- 9. Stochastic Programming and Optimization in Horserace Betting William T. Ziemba -- 1 Introduction -- 2 The importance of getting the mean right -- 3 The favorite-longshot bias -- 4 Place and show optimization with transactions costs -- 5 The place pick all -- 6 Some stochastic programming formulations -- 7 The Pick3 and Pick4: Theory of pricing the bets -- 8 ThePick4 -- 9 Example of Pick4 with embedded Pick3's and Doubles: Travers Day at Saratoga -- 10 The Pick6: Theory of pricing the bets -- 11 The one that got away: the hittable 2 million Pick 6 at the 2009 Breeders' Cup -- 12 Professional racetrack betting syndicates -- 13 Conclusion -- References -- Part II. Papers in Production Planning and Logistics.
10. Multi-Stage Stochastic Programming for Natural Gas Infrastructure Design with a Production Perspective Lars Hellemo, Kjetil Midthun, Asgeir Tomasgard and Adrian Werner -- 1 Introduction -- 2 Literature review -- 3 Uncertainty -- 3.1 Uncertainty in the context of our model -- 3.2 The multi-horizon scenario tree -- 4 Modelstructure -- 4.1 Time structure, investment and operational decisions -- 4.2 Modularity -- 5 Coremodel -- 5.1 Objective function -- 5.2 Investment constraints -- 5.3 Operational constraints -- 5.4 Objective function terms -- 6 Selected extension modules -- 6.1 Pressure dynamics -- 6.2 Reservoir modeling -- 6.3 Quality/multi-component flow modeling -- 7 Case study -- 8 Conclusions -- Acknowledgments -- References -- A Notation -- A.1 Sets and indices -- A.2 Decision variables -- A.3 Variables/functions -- A.4 Parameters/constants -- A.5 Profiles -- 11. A Stochastic Programming Model for Optimizing the Production of Farmed Atlantic Salmon Martin B. Hæreid, Peter Schutz and Asgeir Tomasgard -- 1 Introduction -- 2 Salmon Farming -- 2.1 Production in seawater -- 2.2 Uncertainty in production -- 2.2.1 Biomass development -- 2.2.2 Loss in production -- 2.2.3 Consequences of the uncertainty in biomass development -- 2.3 The Norwegian regulatory framework -- 3 The Market for Atlantic Salmon -- 3.1 Supply -- 3.2 Price -- 3.3 Other sources of uncertainty -- 4 Biomass Growth Model -- 5 Model Formulation -- 5.1 Model properties -- 5.2 Notation -- 5.3 Stochastic variables and time structure -- 5.4 Mathematical formulation -- 5.4.1 Objective function -- 5.4.2 Constraints -- 6 Conclusions -- References -- 12. Prioritizing Network Interdiction of Nuclear Smuggling Dennis P. Michalopoulos, David P. Morton and J. Wesley Barnes -- 1 Introduction -- 2 Computing detection probabilities -- 3 Prioritized bipartite stochastic network interdiction.
3.1 Model assumptions -- 3.2 Formulation -- 4 The value of prioritization -- 5 Improving the formulation of PrBiSNIP -- 5.1 Restricting the size of Kω -- 5.2 Threat scenario aggregation -- 5.3 Row generation algorithm -- 6 Computational experiments and results -- 6.1 Russian model -- 6.2 US model -- 6.3 Heuristic generation of granular priority lists -- 7 Conclusion -- Acknowledgements -- References -- 13. Saw mill Production Planning Under Uncertainty: Modelling and Solution Approaches Masoumeh Kazemi Zanjani, Mustapha Nourelfath and Daoud Ait-Kadi -- 1 Introduction -- 2 Production planning in the sawing units of sawmill -- 2.1 Sawing process in sawmills -- 2.2 A deterministic LP model for sawmill production planning -- 2.2.1 Notation -- 2.2.2 The deterministic LP model -- 3 Production planning in sawing units by taking into account the random yield -- 3.1 Modelling the random process yields -- 3.2 A two-stage stochastic model with recourse for sawmill production planning -- 3.3 Validation of the stochastic sawmill production planning model by Monte Carlo simulation -- 3.4 Application of the proposed stochastic production planning model for a prototype sawmill -- 3.4.1 Prototype sawmill -- 3.4.2 Comparison between the stochastic and deterministic sawmill production planning models -- 3.5 Taking into account service robustness in the stochastic sawmill production planning model -- 3.5.1 Robust optimization models for sawmill production planning -- 3.5.1.1 Notations -- 3.5.1.2 The robust optimization models -- 3.5.2 Application of robust optimization approach for the sawmill example -- 3.5.2.1 RO-(UPM-2) model results -- 3.5.2.2 RO-(UPV) model results -- 3.5.2.3 Performance comparison between RO-(UPM-2) and RO-UPV models -- 4 Production planning in sawing units by taking into account the random yield and random demand.
4.1 Modelling the uncertain yield and demand.
Summary: This book shows the breadth and depth of stochastic programming applications. All the papers presented here involve optimization over the scenarios that represent possible future outcomes of the uncertainty problems. The applications, which were presented at the 12th International Conference on Stochastic Programming held in Halifax, Nova Scotia in August 2010, span the rich field of uses of these models. The finance papers discuss such diverse problems as longevity risk management of individual investors, personal financial planning, intertemporal surplus management, asset management with benchmarks, dynamic portfolio management, fixed income immunization and racetrack betting. The production and logistics papers discuss natural gas infrastructure design, farming Atlantic salmon, prevention of nuclear smuggling and sawmill planning. The energy papers involve electricity production planning, hydroelectric reservoir operations and power generation planning for liquid natural gas plants. Finally, two telecommunication papers discuss mobile network design and frequency assignment problems.
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Intro -- Contents -- Acknowledgements -- List of Contributors -- Preface -- Books and Collections of Papers on Stochastic Programming -- 1. Introduction and Summary -- Part I. Papers in Finance -- 2. Longevity Risk Management for Individual Investors Woo Chang Kim, John M. Mulvey, Koray D. Simsek and Min Jeong Kim -- 1 Introduction -- 2 Model -- 3 Numerical results -- 3.1 First example: Retirement planning without longevity risk consideration -- 3.2 Second example: Impact of longevity risk to retirement planning -- 3.3 Third example: Longevity risks in pension benefits -- 4 Conclusions -- References -- 3. Optimal Stochastic Programming-Based Personal Financial Planning with Intermediate and Long-Term Goals Vittorio Moriggia, Giorgio Consigli and Gaetano Iaquinta -- 1 Introduction -- 2 The asset-liability management model -- 2.1 Individual wealth, consumption and investment targets -- 2.2 Random coefficients and scenarios -- 2.3 The optimization problem -- 3 Numerical implementation and case study -- 3.1 Decision tool modular structure -- 3.1.1 Individual policy statement -- 3.1.2 Scenario manager -- 3.1.3 Output -- 3.2 Case study -- 3.2.1 Optimal solutions -- 4 Conclusion -- References -- 4. Intertemporal Surplus Management with Jump Risks Mareen Benk -- 1 Introduction -- 2 An intertemporal surplus management model with jump risks - a three-fund theorem -- 3 Risk preference, and funding ratio -- 4 Conclusions -- Appendix I: Derivation of the asset specific risk factor of the first jump component -- Appendix II: Derivation of equation (16) -- Appendix III: Derivation of equation (17) -- References -- 5. Jump-Diffusion Risk-Sensitive Benchmarked Asset Management Mark Davis and Sebastien Lleo -- 1 Introduction -- 2 Analytical setting -- 2.1 Factor dynamics -- 2.2 Asset market dynamics -- 2.3 Benchmark modelling -- 2.4 Portfolio dynamics.

2.5 Investment constraints -- 2.6 Problem formulation -- 3 Dynamic programming and the value function -- 3.1 The risk-sensitive control problems under Ph -- 3.2 Properties of the value function -- 3.3 Main result -- 4 Existence of a classical (C1,2) solution under affine drift assumptions -- 5 Existence of a classical (C1,2) solution under standard control assumptions -- 6 Verification -- 6.1 The unique maximizer of the supremum (60) is the optimal control, i.e. h*(t,Xt) = h (t,Xt,D (t,Xt)) -- 6.2 Verification -- 7 Conclusion -- References -- 6. Dynamic Portfolio Optimization under Regime-Based Firm Strength Chanaka Edirisinghe and Xin Zhang -- 1 Introduction -- 2 DEA-based relative firm strength -- 2.1 Financial DEA model -- 2.2 Parameters of RFS -- 2.3 Correlation analysis -- 3 Modeling market regimes -- 3.1 Regime analysis (1971-2010) -- 3.2 Regime-based firm-RFS -- 4 Portfolio optimization under regime-based RFS -- 4.1 RFS-based stock selections -- 4.2 Decisions under regime-scenarios -- 4.3 Transactions cost model -- 4.4 Budget constraints -- 4.5 Risk-return framework -- 4.6 Two-period optimization model -- 5 Model application -- 5.1 RFS estimation and firm selections -- 5.2 Portfolio analysis -- 6 Conclusions -- Acknowledgement -- References -- 7. Options Portfolio Management as a Chance Constrained Problem Dmitry Golembiovsky and Anatoliy Abramov -- 1 Introduction -- 2 Model of options market -- 3 A scenario model for stochastic programming -- 4 The problem of option portfolio optimization -- 5 Solving the problem and some simulation results -- 6 Conclusions and future research -- References -- 8. Stochastic Models for Optimizing Immunization Strategies in Fixed-Income Security Portfolios under Some Sources of Uncertainty Larraitz Aranburu, Laureano F. Escudero, M. Araceli Garin and Gloria Perez -- 1 Introduction.

2 The deterministic LP optimization model -- 3 Two sources of uncertainty: interest rate and credit risk -- 4 Traditional two-stage stochastic optimization approach -- 5 Risk adverse models -- 5.1 Mean-risk immunization strategy -- 5.2 Value-at-Risk (VaR) strategy -- 5.3 Stochastic dominance strategy -- 6 Two-stage fixed-income security portfolio immunization based on the VaR strategy -- 7 A more accurate solution: a multistage stochastic scheme -- 7.1 Multistage maxmin immunization strategy -- 7.2 Multistage stochastic dominance strategy -- 7.3 Multistage VaR & stochastic dominance strategy -- 8 Case study -- 8.1 Deterministic LP model -- 8.2 Two-stage scheme -- 8.3 Two-stage stochastic model (DEM1) -- 8.4 Mean-risk immunization model (DEM-MR) -- 8.5 Two-stage maxmin immunization model (DEM2) -- 8.6 Two-stage VaR model (DEM3) -- 8.7 Multistage scheme -- 8.8 Multistage maxmin immunization model (DEM4) -- 8.9 Multistage stochastic dominance model (DEM5) -- 8.10 Multistage VaR & stochastic dominance model (DEM6) -- 9 Models comparison and conclusions -- References -- 9. Stochastic Programming and Optimization in Horserace Betting William T. Ziemba -- 1 Introduction -- 2 The importance of getting the mean right -- 3 The favorite-longshot bias -- 4 Place and show optimization with transactions costs -- 5 The place pick all -- 6 Some stochastic programming formulations -- 7 The Pick3 and Pick4: Theory of pricing the bets -- 8 ThePick4 -- 9 Example of Pick4 with embedded Pick3's and Doubles: Travers Day at Saratoga -- 10 The Pick6: Theory of pricing the bets -- 11 The one that got away: the hittable 2 million Pick 6 at the 2009 Breeders' Cup -- 12 Professional racetrack betting syndicates -- 13 Conclusion -- References -- Part II. Papers in Production Planning and Logistics.

10. Multi-Stage Stochastic Programming for Natural Gas Infrastructure Design with a Production Perspective Lars Hellemo, Kjetil Midthun, Asgeir Tomasgard and Adrian Werner -- 1 Introduction -- 2 Literature review -- 3 Uncertainty -- 3.1 Uncertainty in the context of our model -- 3.2 The multi-horizon scenario tree -- 4 Modelstructure -- 4.1 Time structure, investment and operational decisions -- 4.2 Modularity -- 5 Coremodel -- 5.1 Objective function -- 5.2 Investment constraints -- 5.3 Operational constraints -- 5.4 Objective function terms -- 6 Selected extension modules -- 6.1 Pressure dynamics -- 6.2 Reservoir modeling -- 6.3 Quality/multi-component flow modeling -- 7 Case study -- 8 Conclusions -- Acknowledgments -- References -- A Notation -- A.1 Sets and indices -- A.2 Decision variables -- A.3 Variables/functions -- A.4 Parameters/constants -- A.5 Profiles -- 11. A Stochastic Programming Model for Optimizing the Production of Farmed Atlantic Salmon Martin B. Hæreid, Peter Schutz and Asgeir Tomasgard -- 1 Introduction -- 2 Salmon Farming -- 2.1 Production in seawater -- 2.2 Uncertainty in production -- 2.2.1 Biomass development -- 2.2.2 Loss in production -- 2.2.3 Consequences of the uncertainty in biomass development -- 2.3 The Norwegian regulatory framework -- 3 The Market for Atlantic Salmon -- 3.1 Supply -- 3.2 Price -- 3.3 Other sources of uncertainty -- 4 Biomass Growth Model -- 5 Model Formulation -- 5.1 Model properties -- 5.2 Notation -- 5.3 Stochastic variables and time structure -- 5.4 Mathematical formulation -- 5.4.1 Objective function -- 5.4.2 Constraints -- 6 Conclusions -- References -- 12. Prioritizing Network Interdiction of Nuclear Smuggling Dennis P. Michalopoulos, David P. Morton and J. Wesley Barnes -- 1 Introduction -- 2 Computing detection probabilities -- 3 Prioritized bipartite stochastic network interdiction.

3.1 Model assumptions -- 3.2 Formulation -- 4 The value of prioritization -- 5 Improving the formulation of PrBiSNIP -- 5.1 Restricting the size of Kω -- 5.2 Threat scenario aggregation -- 5.3 Row generation algorithm -- 6 Computational experiments and results -- 6.1 Russian model -- 6.2 US model -- 6.3 Heuristic generation of granular priority lists -- 7 Conclusion -- Acknowledgements -- References -- 13. Saw mill Production Planning Under Uncertainty: Modelling and Solution Approaches Masoumeh Kazemi Zanjani, Mustapha Nourelfath and Daoud Ait-Kadi -- 1 Introduction -- 2 Production planning in the sawing units of sawmill -- 2.1 Sawing process in sawmills -- 2.2 A deterministic LP model for sawmill production planning -- 2.2.1 Notation -- 2.2.2 The deterministic LP model -- 3 Production planning in sawing units by taking into account the random yield -- 3.1 Modelling the random process yields -- 3.2 A two-stage stochastic model with recourse for sawmill production planning -- 3.3 Validation of the stochastic sawmill production planning model by Monte Carlo simulation -- 3.4 Application of the proposed stochastic production planning model for a prototype sawmill -- 3.4.1 Prototype sawmill -- 3.4.2 Comparison between the stochastic and deterministic sawmill production planning models -- 3.5 Taking into account service robustness in the stochastic sawmill production planning model -- 3.5.1 Robust optimization models for sawmill production planning -- 3.5.1.1 Notations -- 3.5.1.2 The robust optimization models -- 3.5.2 Application of robust optimization approach for the sawmill example -- 3.5.2.1 RO-(UPM-2) model results -- 3.5.2.2 RO-(UPV) model results -- 3.5.2.3 Performance comparison between RO-(UPM-2) and RO-UPV models -- 4 Production planning in sawing units by taking into account the random yield and random demand.

4.1 Modelling the uncertain yield and demand.

This book shows the breadth and depth of stochastic programming applications. All the papers presented here involve optimization over the scenarios that represent possible future outcomes of the uncertainty problems. The applications, which were presented at the 12th International Conference on Stochastic Programming held in Halifax, Nova Scotia in August 2010, span the rich field of uses of these models. The finance papers discuss such diverse problems as longevity risk management of individual investors, personal financial planning, intertemporal surplus management, asset management with benchmarks, dynamic portfolio management, fixed income immunization and racetrack betting. The production and logistics papers discuss natural gas infrastructure design, farming Atlantic salmon, prevention of nuclear smuggling and sawmill planning. The energy papers involve electricity production planning, hydroelectric reservoir operations and power generation planning for liquid natural gas plants. Finally, two telecommunication papers discuss mobile network design and frequency assignment problems.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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