Eberle, Stefan (2009): A Polynomial Algorithm for a NPhard to solve Optimization Problem. Dissertation, LMU München: Faculty of Physics 

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Abstract
Since Markowitz in 1952 described an efficient and practical way of finding the optimal portfolio allocation in the normal distributed case, a lot of progress in several directions has been made. The main objective of this thesis is to replace the original risk measure of the Markowitz setting by a more suitable one, ValueatRisk. In adressing the optimal allocation problem in a slightly more general setting, thereby still allowing for a large number of different asset classes, an efficient algorithm is developed for finding the exact solution in the case of specially distributed losses. Applying this algorithm to even more general loss distributions results in a not necessarily exact matching of the VaR optimum. However, in this case, upper bounds for the euclidean distance between the exact optimum and the output of the proposed algorithm are given. An investigation of these upper bounds shows, that in general the algorithm results in quite good approximations to the VaR optimum. Finally, an application of a stochastic branch & bound algorithm to the current problem is discussed.
Item Type:  Thesis (Dissertation, LMU Munich) 

Keywords:  Value at Risk Conditional Value at Risk Optimization 
Subjects:  600 Natural sciences and mathematics 600 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date Accepted:  29. January 2009 
1. Referee:  Richert, Walter 
Persistent Identifier (URN):  urn:nbn:de:bvb:1999427 
MD5 Checksum of the PDFfile:  0d1d36b1eaa59884a79243217a24c67c 
Signature of the printed copy:  0001/UMC 17713 
ID Code:  9942 
Deposited On:  17. Apr 2009 09:03 
Last Modified:  16. Oct 2012 08:27 