The paper studies problem of optimal portfolio selection. It is shown that, under some mild conditions, near optimal strategies for investors with different performance criteria can be constructed using a limited number of fixed processes (mutual funds), for a market with a larger number of available risky stocks. This implies dimension reduction for the optimal portfolio selection problem: all rational investors may achieve optimality using the same mutual funds plus a saving account. This result is obtained under mild restrictions for the utility functions without any assumptions on regularity of the value function. The proof is based on the method of dynamic programming applied indirectly to some convenient approximations of the original problem that ensure certain regularity of the value functions. To overcome technical difficulties, we use special time dependent and random constraints for admissible strategies such that the corresponding HJB (Hamilton–Jacobi–Bellman) equation admits “almost explicit” solutions generating near optimal admissible strategies featuring sufficient regularity and integrability.

Accepted:

DOI: 10.1051/cocv/2017013

Keywords: Stochastic control, near optimal strategies portfolio structure, dimension reduction, Mutual Funds Theorem

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@article{COCV_2018__24_3_1043_0, author = {Dokuchaev, Nikolai}, title = {On the structure of multifactor optimal portfolio strategies}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1043--1058}, publisher = {EDP-Sciences}, volume = {24}, number = {3}, year = {2018}, doi = {10.1051/cocv/2017013}, mrnumber = {3877192}, zbl = {1418.91464}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2017013/} }

TY - JOUR AU - Dokuchaev, Nikolai TI - On the structure of multifactor optimal portfolio strategies JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 1043 EP - 1058 VL - 24 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2017013/ DO - 10.1051/cocv/2017013 LA - en ID - COCV_2018__24_3_1043_0 ER -

%0 Journal Article %A Dokuchaev, Nikolai %T On the structure of multifactor optimal portfolio strategies %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 1043-1058 %V 24 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2017013/ %R 10.1051/cocv/2017013 %G en %F COCV_2018__24_3_1043_0

Dokuchaev, Nikolai. On the structure of multifactor optimal portfolio strategies. ESAIM: Control, Optimisation and Calculus of Variations, Volume 24 (2018) no. 3, pp. 1043-1058. doi : 10.1051/cocv/2017013. http://archive.numdam.org/articles/10.1051/cocv/2017013/

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