A derivation of conventional portfolios and a new linear utility method

Author

Gashi, Bujar

Author_Institution

Sch. of Inf. Syst., Comput. & Math., Brunei Univ., Uxbridge

fYear

2006

fDate

14-16 June 2006

Abstract

Four known portfolios are derived using a new control theory approach. These are the mean-variance, the HARA utility, the log-optimal and the exponential utility portfolios. A single HJB equation is derived from the dynamics of the wealth logarithm. The value functions for different portfolios appear as solutions to this single equation, and thus unifying the derivation of the mean-variance and the other three portfolios. A new method for portfolio selection is proposed that uses the linear utility and penalizes the fractions of wealth allocated across the risky assets. Conventional portfolios appear as examples to this more general method

Keywords

control theory; financial management; matrix algebra; risk management; utility theory; HARA utility; HJB equation; control theory; exponential utility portfolio; linear utility method; log-optimal portfolio; mean-variance portfolio; portfolio selection; value functions; wealth logarithm; Equations; Information analysis; Information systems; Investments; Mathematical model; Mathematics; Optimization methods; Portfolios; Regulators; Risk analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2006

Conference_Location

Minneapolis, MN

Print_ISBN

1-4244-0209-3

Electronic_ISBN

1-4244-0209-3

Type

conf

DOI

10.1109/ACC.2006.1655492

Filename

1655492