Sustainable Asset Accumulation and Dynamic Portfolio Decisions by Carl Chiarella Willi Semmler Chih-Ying Hsiao & Lebogang Mateane

Author:Carl Chiarella, Willi Semmler, Chih-Ying Hsiao & Lebogang Mateane
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

5.3 The Dynamic Programming Solution

Next, we employ our dynamic programming method because this allows us to circumvent some of the short comings of the Campbell and Viceira procedure. We solve for the optimal consumption, C t , and the asset allocation weight, α, for a more general setting. In order to simplify, and avoid a three dimensional state space, we consider only equity returns and the real interest rate. Note that in contrast to Campbell and Viceira (2002, Chap. 3) we can, with our solution procedure, allow for time varying returns, represented by our estimated low frequency movements of returns, using the harmonic estimations of Hsiao and Semmler (2009). In this context, the expected excess return can be allowed to vary and the fraction of assets allocated to risky assets are permitted to be time varying.

Given this set-up, it is then interesting what difference one obtains across investors with different risk aversion. In fact, our procedure allows to explore the effect of the varying risk parameter, γ, on consumption, C t , the weight for the equity choice, α t , the build up and the fate of wealth and permits to evaluate the welfare, W t , of the investors.

The DP problem of our approach can be stated as follows:

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