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Long-Term Portfolio Choice Given Uncertain Personal Savings

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Investors choosing a portfolio strategy, in order to secure a pension at a future date forexample, are faced with many uncertainties. One major uncertainty is the amount bywhich their pension fund will be supplemented by personal savings from a variety of sourcessuch as life insurance contracts, bequests, or property sales. Over long periods of time theseuncertainties are likely to be large and difficult to hedge, and hence may have a significanteffect on the dynamic portfolio strategy. Drawing on the results of previous literature on thereaction of investors to non-unhedgeable background risk, and on the theory of stochasticdynamic programming, this article derives optimal strategies for investors maximising theexpected utility of terminal wealth, where this wealth consists of the value of a pensionfund plus accumulated personal savings. Numerical results, assuming that the marketportfolio and the expectation of personal savings follow (possibly) correlated geometricBrownian motions, are derived to illustrate the effects of the size and uncertainty of thepersonal savings, as well as the effect of the resolution of the uncertainty in them overtime. The computation uses a new technique for implementing the stochastic dynamicprogramming. This involves a binomial approximation, in two dimensions, which ensuresthat the computations are feasible for relatively long-term problems.

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Guenter Franke, Sandra Peterson, Richard C. Stapleton

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