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Discrete-Time Financial Planning Models Under Loss-Averse Preferences

Department of Finance, Vrije Universiteit Amsterdam, De Boelelaan 1105, NL, Amsterdam, The Netherlands, and Research Department, Netherlands Central Bank (DNB)
Department of Finance, Vrije Universiteit Amsterdam, De Boelelaan 1105, NL, Amsterdam, The Netherlands, and Tinbergen Institute, Amsterdam, The Netherlands
asiegmann{at}feweb.vu.nl
alucas{at}feweb.vu.nl

We consider a dynamic asset allocation problem formulated as a mean-shortfall model in discrete time. A characterization of the solution is derived analytically under general distributional assumptions for serially independent risky returns. The solution displays risk taking under shortfall, as well as a specific form of time diversification. Also, for a representative stock-return distribution, risk taking increases monotonically with the number of decision moments given a fixed horizon. This is related to the well-known casino effect arising in a downside-risk and expected return framework. As a robustness check, we provide results for a modified objective with a quadratic penalty on shortfall. An analytical solution for a single-stage setup is derived, and numerical results for the two-period model and time diversification are provided.

Subject classifications: multistage stochastic programming; downside risk; asset/liability management; time diversification.
History: Received November 2002; revision received February 2004; accepted April 2004.