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Stochastic Dedication: Designing Fixed Income Portfolios Using Massively Parallel Benders Decomposition

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Author Info

  • Randall S. Hiller

    (Delta Global Trading LP, 4 Cambridge Center, Cambridge, Massachusetts 02142)

  • Jonathan Eckstein

    (Mathematical Sciences Research Group, Thinking Machines Corporation, 245 First Street, Cambridge, Massachusetts 02142)

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    Abstract

    Drawing on recent developments in discrete time fixed income options theory, we propose a stochastic programming procedure, which we call stochastic dedication, for managing asset/liability portfolios with interest rate contingent claims. The model uses scenario generation to combine deterministic dedication techniques with stochastic duration matching methods, and provides the portfolio manager with a risk/return Pareto optimal frontier from which a portfolio may be selected based on individual risk attitudes. We employ a fixed income risk metric that can be interpreted as the fair market value of a collection of interest rate options that eliminates bankruptcy risk from the asset/liability portfolio. We incorporate this metric into a risk/return stochastic optimization model, using a binomial lattice sampling procedure to construct interest rate paths and cash flow streams from an arbitrage-free term structure model. The resulting parametric linear program has a particularly simple subproblem structure, and we have been able to solve it using resource-directed decomposition on a massively parallel computer system, the Connection Machine CM-2. We take a novel approach that uses a standard serial simplex method to solve the master problem, but generates scenarios and Benders cuts in a massively parallel manner. We discuss the performance of this implementation and present the results for a simple pension fund immunization problem.

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    File URL: http://dx.doi.org/10.1287/mnsc.39.11.1422
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 39 (1993)
    Issue (Month): 11 (November)
    Pages: 1422-1438

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    Handle: RePEc:inm:ormnsc:v:39:y:1993:i:11:p:1422-1438

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    Related research

    Keywords: finance; portfolios; stochastic programming; Benders decomposition; computers; parallel; decision analysis; risk;

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    Cited by:
    1. Benati, Stefano & Rizzi, Romeo, 2007. "A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem," European Journal of Operational Research, Elsevier, vol. 176(1), pages 423-434, January.
    2. Klaassen, Pieter, 1997. "Solving stochastic programming models for asset/liability management using iterative disaggregation," Serie Research Memoranda 0010, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    3. Klaassen, Pieter, 1997. "Discretized reality and spurious profits in stochastic programming models for asset/liability management," European Journal of Operational Research, Elsevier, vol. 101(2), pages 374-392, September.
    4. Wong, Man Hong, 2013. "Investment models based on clustered scenario trees," European Journal of Operational Research, Elsevier, vol. 227(2), pages 314-324.
    5. Oguzsoy, Cemal Berk & Guven, Sibel, 1997. "Bank asset and liability management under uncertainty," European Journal of Operational Research, Elsevier, vol. 102(3), pages 575-600, November.
    6. Arjen Siegmann, 2003. "Optimal Investment Policies for Defined Benefit Pension Funds," DNB Staff Reports (discontinued) 112, Netherlands Central Bank.
    7. Dupacova, Jitka & Bertocchi, Marida, 2001. "From data to model and back to data: A bond portfolio management problem," European Journal of Operational Research, Elsevier, vol. 134(2), pages 261-278, October.
    8. Vladimirou, Hercules, 1998. "Computational assessment of distributed decomposition methods for stochastic linear programs," European Journal of Operational Research, Elsevier, vol. 108(3), pages 653-670, August.
    9. Klaassen, Pieter, 1997. "Discretized reality and spurious profits in stochastic programming models for asset/liability management," Serie Research Memoranda 0011, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.

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