Convergence of the embedded mean-variance optimal points with discrete sampling

نویسندگان

  • Duy-Minh Dang
  • Peter A. Forsyth
  • Yuying Li
چکیده

5 A numerical technique based on the embedding technique proposed in [21, 33] for dynamic 6 mean-variance (MV) optimization problems may yield spurious points, i.e. points which are not 7 on the efficient frontier. In [27], it is shown that spurious points can be eliminated by examining 8 the left upper convex hull of the solution of the embedded problem. However, any numerical 9 algorithm will generate only a discrete sampling of the solution set of the embedded problem. In 10 this paper, we formally establish that, under mild assumptions, every limit point of a suitably 11 defined sequence of upper convex hulls of the sampled solution of the embedded problem is on the 12 original MV efficient frontier. For illustration, we discuss an MV asset-liability problem under 13 jump diffusions, which is solved using a numerical Hamilton-Jacobi-Bellman partial differential 14 equation approach. 15

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عنوان ژورنال:
  • Numerische Mathematik

دوره 132  شماره 

صفحات  -

تاریخ انتشار 2016