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A two-stage stochastic integer programming approach

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  • Merino Maestre, María
  • Pérez Sainz de Rozas, Gloria
  • Escudero Bueno, Laureano F.
  • Garín Martín, María Araceli

Abstract

We present an algorithmic approach for solving two-stage stochastic mixed 0-1 problems. The first stage constraints of the Deterministic Equivalent Model have 0--1 variables and continuous variables. The approach uses the Twin Node Family (TNF) concept within the algorithmic framework so-called {Branch-and-Fix Coordination} for satisfying the {nonanticipativity} constraints, jointly with a Benders Decomposition scheme for solving a given {LP} model at each {TNF} integer set. As an illustrative case, the structuring of a portfolio of Mortgage-Backed Securities under uncertainty in the interest rate path along a given time horizon is used. Some computational experience is reported.

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Paper provided by Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística) in its series BILTOKI with number 2005-01.

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Date of creation: 2005
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Handle: RePEc:ehu:biltok:200501

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Postal: Dpto. de Econometría y Estadística, Facultad de CC. Económicas y Empresariales, Universidad del País Vasco, Avda. Lehendakari Aguirre 83, 48015 Bilbao, Spain
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Keywords: two stage programming; Benders decomposition; branch-and-fix coordination;

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  1. Pan Kang & Stavros A. Zenios, 1992. "Complete Prepayment Models for Mortgage-Backed Securities," Management Science, INFORMS, vol. 38(11), pages 1665-1685, November.
  2. Francis A. Longstaff, 2004. "Optimal Recursive Refinancing and the Valuation of Mortgage-Backed Securities," NBER Working Papers 10422, National Bureau of Economic Research, Inc.
  3. Dunn, Kenneth B & McConnell, John J, 1981. "Valuation of GNMA Mortgage-Backed Securities," Journal of Finance, American Finance Association, vol. 36(3), pages 599-616, June.
  4. Deng, Yongheng & Quigley, John M. & Van Order, Robert, 1999. "Mortgage Terminations, Heterogeneity, and the Exercise of Mortgage Options," Berkeley Program on Housing and Urban Policy, Working Paper Series qt96r560pg, Berkeley Program on Housing and Urban Policy.
  5. Lockett, A. Geoffrey & Gear, Anthony E., 1975. "Multistage Capital Budgeting under Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 10(01), pages 21-36, March.
  6. Fleten, Stein-Erik & Hoyland, Kjetil & Wallace, Stein W., 2002. "The performance of stochastic dynamic and fixed mix portfolio models," European Journal of Operational Research, Elsevier, vol. 140(1), pages 37-49, July.
  7. Schwartz, Eduardo S & Torous, Walter N, 1989. " Prepayment and the Valuation of Mortgage-Backed Securities," Journal of Finance, American Finance Association, vol. 44(2), pages 375-92, June.
  8. John M. Mulvey & Hercules Vladimirou, 1992. "Stochastic Network Programming for Financial Planning Problems," Management Science, INFORMS, vol. 38(11), pages 1642-1664, November.
  9. Stanton, Richard, 1995. "Rational Prepayment and the Valuation Mortgage-Backed Securities," Review of Financial Studies, Society for Financial Studies, vol. 8(3), pages 677-708.
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