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Application of sum of squares approximate dynamic programming in multi-period investment

Author(s):

L. Studer
Conference/Journal:

Semester Thesis, HS13 (10307)
Abstract:

This semester project investigates the viability of quartic approximate value functions for a stochastic control problem by nding lower bounds. The underlying stochastic control problem is the multi-period investment problem with (QP-representable) transaction cost. Several constraints on the portfolio are discussed. Then, the theory behind the lower bound/basis function ADP method is reviewed and applied to the case of multivariate polynomials of total degree up to 4. An elegant formulation in terms of sum of squares optimization problems is introduced and implemented for the discussed portfolio constraints. However, the results are not in favor of using quartic approximations. A theorem is developed which shows that under practical conditions, and for this speci c problem formulation, no quartic/cubic solution should be expected.

Year:

2013
Type of Publication:

(13)Semester/Bachelor Thesis
Supervisor:

T.H. Summers

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% Autogenerated BibTeX entry
@PhdThesis { Xxx:2013:IFA_4579
}
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