A stochastic programming model for money management.

*(English)*Zbl 0912.90020Summary: Portfolio managers in the new fixed-income securities have to cope with various forms of uncertainty, in addition to the usual interest rate changes. Uncertainty in the timing and amount of cashflows, changes in the default and other risk premia and so on, complicate the portfolio manager’s problem. We develop here a multi-period, dynamic, portfolio optimization model to address this problem. The model specifies a sequence of investment decisions over time that maximize the expected utility of return at the end of the planning horizon. The model is a two-stage stochastic program with recourse. The dynamics of interest rates, cashflow uncertainty, and liquidity, default and other risk premia, are explicitly modeled through postulated scenarios. Simulation procedures are developed to generate these scenarios. The optimization models are then integrated with the simulation procedures. Extensive validation experiments are carried out to establish the effectiveness of the model in dealing with uncertainty. In particular the model is compared against the popular portfolio immunization strategy, and against a portfolio based on mean-absolute deviation optimization.

##### MSC:

91B28 | Finance etc. (MSC2000) |

90C90 | Applications of mathematical programming |

90B90 | Case-oriented studies in operations research |

90C15 | Stochastic programming |

##### Keywords:

fixed income; simulation; multi-period, dynamic, portfolio optimization; cashflow uncertainty##### Software:

GAMS
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\textit{B. Golub} et al., Eur. J. Oper. Res. 85, No. 2, 282--296 (1995; Zbl 0912.90020)

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##### References:

[1] | Babbel, D.F.; Zenios, S.A., Pitfalls in the analysis of option-adjusted spreads, Financial analysts journal, 65-69, (1992), July/August |

[2] | Ben-Dov, Y.; Hayre, L.; Pica, V., Mortgage valuation models at prudential securities, Interfaces, 22, 55-71, (1992) |

[3] | Black, F.; Derman, E.; Toy, W., A one-factor model of interest rates and its application to treasury bond options, Financial analysts journal, 33-39, (1990), January/February |

[4] | Bradley, S.P.; Crane, D.B., A dynamic model for bond portfolio management, Management science, 19, 139-151, (1972) |

[5] | Brooke, A.; Kendrick, D.; Meeraus, A., GAMS: A User’s guide, (1988) |

[6] | Cagan, L.D.; Carriero, N.S.; Zenios, S.A., Pricing mortgage-backed securities with network linda, Financial analysts journal, 55-62, (1993), March/April |

[7] | Carino, D.R.; Kent, T.; Myers, D.H.; Stacy, C.; Sylvanus, M.; Turner, A.; Watanabe, K.; Ziemba, W.T., The russell-Yasuda-kasai model, Interfaces, 24, 1, 29-49, (1994) |

[8] | Grauer, R.R.; Hakansson, N.H., Returns on levered actively managed long-run portfolios of stocks, bonds and bills, Financial analysts journal, 24-43, (1985), September |

[9] | Hiller, R.S., and Eckstein, J., “Stochastic dedication: Designing fixed income portfolios using massively parallel Benders decompositionâ€ť, Management Science, to appear. · Zbl 0800.90064 |

[10] | Holmer, M.R., The asset/liability management system at fannie mae, Interfaces, 24, 3, 3-21, (1994) |

[11] | Hutchinson, J.M.; Zenios, S.A., Financial simulations on a massively parallel connection machine, International journal of supercomputer applications, 5, 2, 27-45, (1991) |

[12] | Ingersoll, J.E., Theory of financial decision making, () |

[13] | Kang, P.; Zenios, S.A., Complete prepayment models for mortgage backed securities, Management science, 38, 11, 1665-1685, (1992) |

[14] | Konno, H.; Yamazaki, H., Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market, Management science, 37, 5, 519-531, (1991) |

[15] | Kusy, M.I.; Ziemba, W.T., A bank asset and liability management model, Operations research, 34, 3, 356-376, (1986) |

[16] | Maloney, K.M.; Yawitz, J.B., Interest rate risk, immunization, and duration, The journal of portfolio management, 41-48, (1986), Spring |

[17] | Markowitz, H., Mean-variance analysis in portfolio choice and capital markets, (1987), Basil Blackwell Oxford · Zbl 0757.90003 |

[18] | McKendall, R.A.; Zenios, S.A., Computing price paths of mortgage-backed securities using massively parallel computing, (), 374-407 |

[19] | Mossin, J., Optimal multiperiod portfolio policies, Journal of business, 41, 215-229, (1987) |

[20] | Mulvey, J.M.; Vladimirou, H., Stochastic network programming for financial planning problems, Management science, 38, 1643-1664, (1992) · Zbl 0825.90062 |

[21] | Mulvey, J.M.; Zenios, S.A., Diversifying fixed-income portfolios: modeling dynamic effects, Financial analysts journal, 30-38, (1994), January/February |

[22] | Worzel, K.J.; Zenios, C.V.; Zenios, S.A., Integrated simulation and optimization models for tracking fixed-income indices, Operations research, 42, 2, 223-233, (1994) · Zbl 0925.90026 |

[23] | Zenios, S.A., Massively parallel computations for financial modeling under uncertainty, (), 273-294 |

[24] | () |

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