Stochastic Optimization, Tree Structures and Portfolio Choice
نویسندگان
چکیده
Solving realistic dynamic asset allocation problems remains a challenge. While considerable progress with respect to theoretical insights has been made in the past years using dynamic programming, this technique is hardly applicable to deal with industry problems involving numerous sources of uncertainty and path-dependent variables. An alternative solution strategy that has been applied to various applications in finance is Stochastic Linear Programming (SLP). However, what is missing in the literature so far is an extensive evaluation of the influence of different parameters that have to be determined before solving a SLP, namely the tree structure and the procedure of scenario generation. In this paper, we perform such an analysis by setting up an artificial portfolio management problem whose theoretical optimal solution is known. Therefore we can evaluate the accuracy of solutions derived via SLP against this known benchmark. We find that the tree structure plays an important role as long as simple scenario generation techniques are concerned. For sophisticated techniques, which ensure that even for a small number of random draws the first two moments of the distribution are matched, the scenario tree structure is less important. However, for simple Monte Carlo techniques – used in most of the existing research papers – the tree structure might considerably bias the optimal solutions. In such situations, symmetric trees (e.g., 100x100) show best performance.
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تاریخ انتشار 2005