Title:

Mean–Variance Portfolio Optimization with State Dependent Risk Aversion

Author:

Björk, Tomas; Murgoci, Agatha; Zhou, Xun Yu 
Abstract:

The objective of this paper is to study the mean–variance portfolio
optimization in continuous time. Since this problem is time inconsistent
we attack it by placing the problem within a game theoretic framework
and look for subgame perfect Nash equilibrium strategies. This particular
problem has already been studied in [2] where the authors assumed a con
stant risk aversion parameter. This assumption leads to an equilibrium
control where the dollar amount invested in the risky asset is independent
of current wealth, and we argue that this result is unrealistic from an eco
nomic point of view. In order to have a more realistic model we instead
study the case when the risk aversion depends dynamically on current
wealth. This is a substantially more complicated problem than the one
with constant risk aversion but, using the general theory of time inconsis
tent control developed in [4], we provide a fairly detailed analysis on the
general case. In particular, when the risk aversion is inversely proportional
to wealth, we provide an analytical solution where the equilibrium dollar
amount invested in the risky asset is proportional to current wealth. The
equilibrium for this model thus appears more reasonable than the one for
the model with constant risk aversion. 
URI:

http://hdl.handle.net/10398/9097

Date:

20150126 
Notes:

This is the accepted version of the following article: Björk, T., Murgoci, A. and Zhou, X. Y. (2014), MEAN–VARIANCE PORTFOLIO OPTIMIZATION WITH STATEDEPENDENT RISK AVERSION. Mathematical Finance, 24: 1–24., which has been published in final form at doi:
http://dx.doi.org/10.1111/j.14679965.2011.00515.x 