Life-Cycle Asset Allocation and Consumption Using Stochastic Linear Programming

27 Pages Posted: 21 Dec 2006 Last revised: 30 Jan 2018

See all articles by Alois Geyer

Alois Geyer

VGSF / WU

Michael Hanke

University of Liechtenstein

Alex Weissensteiner

Free University of Bolzano Bozen

Date Written: September 10, 2007

Abstract

We consider optimal consumption and (strategic) asset allocation of an investor with uncertain lifetime. The problem is solved using a multi-stage stochastic linear programming (SLP) model to be able to generalize the closed-form solution obtained by Richard (1975). We account for aspects of the application of the SLP approach which arise in the context of life-cycle asset allocation, but are also relevant for other problems of similar structure. The objective is to maximize the expected utility of consumption over the lifetime and of bequest at the time of death of the investor. Since we maximize utility (rather than other objectives which can be implemented more easily) we provide a new approach to optimize the breakpoints required for the linearization of the utility function. The uncertainty of the problem is described by discrete scenario trees. The model solves for the rebalancing decisions in the first few years of the investor's lifetime, accounting for anticipated cash flows in the near future, and applies Richard's closed-form solution for the long, subsequent steady-state period. In our numerical examples we first show that available closed-form solutions can be accurately replicated with the SLP-based approach. Second, we add elements to the problem specification which are usually beyond the scope of closed-form solutions. We find that the SLP approach is well suited to account for these extensions of the classical Merton setting.

Keywords: life-cycle asset allocation, stochastic linear programming, scenario trees

JEL Classification: C61, G11

Suggested Citation

Geyer, Alois and Hanke, Michael and Weissensteiner, Alex, Life-Cycle Asset Allocation and Consumption Using Stochastic Linear Programming (September 10, 2007). Journal of Computational Finance, Vol. 12, No. 4, pp. 29-50, 2009. Available at SSRN: https://ssrn.com/abstract=952956 or http://dx.doi.org/10.2139/ssrn.952956

Alois Geyer (Contact Author)

VGSF / WU ( email )

Welthandelsplatz 1
Institute for Financial Research
Vienna, 1020
Austria

HOME PAGE: http://www.wu.ac.at/~geyer

Michael Hanke

University of Liechtenstein ( email )

Fuerst Franz Josef-Strasse
Vaduz, FL-9490
Liechtenstein

Alex Weissensteiner

Free University of Bolzano Bozen ( email )

Universitätsplatz 1
Bolzano, 39100
+39 0471 013496 (Phone)

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