Relaxations of Approximate Linear Programs for the Real Option Management of Commodity Storage

References

• Adelman D (2004) A price-directed approach to stochastic inventory/routing. Oper. Res. 52(4):499–514.Link, Google Scholar
• Adelman D (2007) Dynamic bid prices in revenue management. Oper. Res. 55(4):647–661.Link, Google Scholar
• Adelman D, Klabjan D (2012) Computing near optimal policies in generalized joint replenishment. INFORMS J. Comput. 24(1):148–164.Link, Google Scholar
• Adelman D, Mersereau A (2013) Dynamic capacity allocation to customers who remember past service. Management Sci. 59(3):592–612.Link, Google Scholar
• Bertsekas DP (2007) Dynamic Programming and Optimal Control, 3rd ed., Vol. 2 (Athena Scientific, Belmont, MA).Google Scholar
• Birge J (2011) Quasi-convex stochastic dynamic programming. Working paper, University of Chicago, Chicago.Google Scholar
• Björk T (2004) Arbitrage Theory in Continuous Time (Oxford University Press, Oxford, Oxfordshire, UK).Crossref, Google Scholar
• Black F (1976) The pricing of commodity contracts. J. Financial Econom. 3(1–2):167–179.Crossref, Google Scholar
• Boogert A, de Jong C (2008) Gas storage valuation using a Monte Carlo method. J. Derivatives 15(3):81–98.Crossref, Google Scholar
• Boogert A, de Jong C (2011/2012) Gas storage valuation using a multifactor price process. J. Energy Markets 4(4):29–52.Crossref, Google Scholar
• Brown DB, Smith JE, Sun P (2010) Information relaxations and duality in stochastic dynamic programs. Oper. Res. 58(4): 785–801.Link, Google Scholar
• Carmona R, Ludkovski M (2010) Valuation of energy storage: An optimal switching approach. Quant. Finance 10(4):359–374.Crossref, Google Scholar
• Chen Z, Forsyth PA (2007) A semi-Lagrangian approach for natural gas storage valuation and optimal operation. SIAM J. Scientific Comput. 30(1):339–368.Crossref, Google Scholar
• Cortazar G, Schwartz ES (1994) The valuation of commodity contingent claims. J. Derivatives 1(4):27–39.Crossref, Google Scholar
• Cortazar G, Gravet M, Urzua J (2008) The valuation of multidimensional American real options using the LSM simulation method. Computers Oper. Res. 35(1):113–129.Crossref, Google Scholar
• de Farias DP, Van Roy B (2001) On constraint sampling for the linear programming approach to approximate dynamic programming. Math. Oper. Res. 29(3):462–478.Link, Google Scholar
• de Farias DP, Van Roy B (2003) The linear programming approach to approximate dynamic programming. Oper. Res. 51(6): 850–865.Link, Google Scholar
• Desai VV, Farias VF, Moallemi CC (2012) Approximate dynamic programming via a smoothed approximate linear program. Oper. Res. 60(3):655–674.Link, Google Scholar
• Devalkar SK, Anupindi R, Sinha A (2011) Integrated optimization of procurement, processing, and trade of commodities. Oper. Res. 59(6):1369–1381.Link, Google Scholar
• Dixit AK, Pindyck RS (1994) Investment Under Uncertainty (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• Eydeland A, Wolyniec K (2003) Energy and Power Risk Management (John Wiley & Sons, Hoboken, NJ).Google Scholar
• Farias VF, Van Roy B (2007) An approximate dynamic programming approach to network revenue management. Working paper, Stanford University, Stanford, CA.Google Scholar
• Felix B, Weber C (2012) Gas storage valuation applying numerically constructed recombining trees. Eur. J. Oper. Res. 216(1):178–187.Crossref, Google Scholar
• Geman H (2005) Commodities and Commodity Derivatives: Modelling and Pricing for Agriculturals, Metals, and Energy (Wiley, Chichester, UK).Google Scholar
• Gray J, Khandelwal P (2004) Towards a realistic gas storage model. Commodities Now (June):1–4.Google Scholar
• Jaillet P, Ronn EI, Tompaidis S (2004) Valuation of commodity-based swing options. Management Sci. 50(7):909–921.Link, Google Scholar
• Lai G, Margot F, Secomandi N (2010) An approximate dynamic programming approach to benchmark practice-based heuristics for natural gas storage valuation. Oper. Res. 58(3):564–582.Link, Google Scholar
• Levy G (2004) Computational Finance: Numerical Methods for Pricing Financial Instruments (Butterworth-Heinemann, Oxford, UK).Google Scholar
• Longstaff FA, Schwartz ES (2001) Valuing American options by simulation: A simple least-squares approach. Rev. Financial Stud. 14(1):113–147.Crossref, Google Scholar
• Manne AS (1960) Linear programming and sequential decisions. Management Sci. 60(3):259–267.Link, Google Scholar
• Maragos S (2002) Valuation of the operational flexibility of natural gas storage reservoirs. Ronn E, ed. Real Options and Energy Management Using Options Methodology to Enhance Capital Budgeting Decisions (Risk Publications, London, UK),431–456.Google Scholar
• Margrabe W (1978) The value of an option to exchange one asset for another. J. Finance 33(1):177–186.Crossref, Google Scholar
• Moallemi CC, Kumar S, Van Roy B (2008) Approximate and data-driven dynamic programming for queuing networks. Working paper, Stanford University, Stanford, CA.Google Scholar
• Morrison JR, Kumar PR (1999) New linear program performance bounds for queuing networks. J. Optim. Theory Appl. 100(3): 575–597.Crossref, Google Scholar
• Munos R (2007) Performance bounds in Lp-norm for approximate value iteration. SIAM J. Control Optim. 46(2):541–561.Crossref, Google Scholar
• Nadarajah S (2014) Approximate dynamic programming for commodity and energy merchant operations. Ph.D. thesis, Carnegie Mellon University, Pittsburgh.Google Scholar
• Petrik M (2012) Distributionally robust approach to approximate dynamic programming. Langford J, Pineau J, eds. Proc. 29th Internat. Conf. Machine Learning, Edinburgh, Scotland, 497–504.Google Scholar
• Petrik M, Zilberstein S (2009) Constraint relaxation in approximate linear programs. Bottou L, Littman M, eds. Proc. 26th Internat. Conf. Machine Learning, Montréal, Québec, 809–816.Crossref, Google Scholar
• Powell WB (2011) Approximate Dynamic Programming: Solving the Curses of Dimensionality, 2nd ed. (John Wiley & Sons, Hoboken, NJ).Crossref, Google Scholar
• Puterman M (1994) Markov Decision Processes: Discrete Stochastic Dynamic Programming (John Wiley & Sons, New York).Crossref, Google Scholar
• Resnick S (1999) A Probability Path (Birkhäuser, Boston).Google Scholar
• Restrepo M (2008) Computational methods for static allocation and real-time redeployment of ambulances. Ph.D. thesis, Cornell University, Ithaca, NY.Google Scholar
• Rubinstein M (1994) Return to OZ. Risk Magazine.Google Scholar
• Schweitzer PJ, Seidmann A (1985) Generalized polynomial approximations in Markovian decision processes. J. Math. Anal. Appl. 110(2):568–582.Crossref, Google Scholar
• Secomandi N (2010) Optimal commodity trading with a capacitated storage asset. Management Sci. 56(3):1090–1049.Link, Google Scholar
• Secomandi N, Lai G, Margot F, Scheller-Wolf A, Seppi DJ (2015) Merchant commodity storage and term-structure model error. Manufacturing Service Oper. Management 17(3):302–320.Link, Google Scholar
• Shreve S (2004) Stochastic Calculus for Finance II: Continuous-Time Models (Springer, New York).Crossref, Google Scholar
• Smith J, McCardle K (1999) Options in the real world: Lessons learned in evaluating oil and gas investments. Oper. Res. 47(1): 1–15.Link, Google Scholar
• Thompson M, Davison M, Rasmussen H (2009) Natural gas storage valuation and optimization: A real options application. Naval Res. Logist. 56(3):226–238.Crossref, Google Scholar
• Topkis D (1998) Supermodularity and Complementarity (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• Trick MA, Zin SE (1997) Spline approximations to value functions. Macroeconomic Dynamics 1(1):255–277.Crossref, Google Scholar
• Tsitsiklis J, Van Roy B (2001) Regression methods for pricing complex American-style options. IEEE Trans. Neural Networks 12(4):694–703.Crossref, Google Scholar
• Veatch MH (2015) Approximate linear programming for networks: Average cost bounds. Computers Oper. Res. 63(November):32–45.Crossref, Google Scholar
• Wu O, Wang D, Qin Z (2012) Seasonal energy storage operations with limited flexibility: The price adjusted rolling intrinsic policy. Manufacturing Service Oper. Management 14(3):455–471.Link, Google Scholar
• Zhang D, Adelman D (2009) An approximate dynamic programming approach to network revenue management with customer choice. Transportation Sci. 43(3):381–394.Link, Google Scholar