Volume 24, Number 3, July–September 2018
|1043 - 1058
|07 June 2018
On the structure of multifactor optimal portfolio strategies
Department of Mathematics & Statistics,Curtin University, GPO Box U198,
6845 Western Australia
2 Department of Information and Navigation Systems, National Research University ITMO, Russia
* Corresponding author: N.Dokuchaev@curtin.edu.au
Revised: 24 March 2016
Accepted: 9 February 2017
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.
Mathematics Subject Classification: 93E20 / 91G10
Key words: Stochastic control / near optimal strategies portfolio structure / dimension reduction / Mutual Funds Theorem
© EDP Sciences, SMAI 2018
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