MEAN–VARIANCE PORTFOLIO OPTIMIZATION WITH STATE‐DEPENDENT RISK AVERSION

By Tomas Björk, Agatha Murgoci, Xun Yu Zhou. 2014

522 citations recorded by the source corpus.

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 Basak and Chabakauri where the authors assumed a constant 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 economic 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‐inconsistent control developed in Björk and Murgoci, 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.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/d1dd521498f15a2c67d72b482fb6edba062221d8

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Citations in the corpus

On time-inconsistent stochastic control in continuous time (2017, unknown): “Other “quadratic” control problems are considered in [2, 6, 8], which study mean-variance problems within the present gametheoretic framework.”
On time-inconsistent stopping problems and mixed strategy stopping times (2018, methodology): “In [5] a meanvariance control problem is studied using the general game-theoretic framework for timeinconsistent stochastic control of [3].”
Equilibrium investment strategy for defined-contribution pension schemes with generalized mean–variance criterion and mortality risk (2015, background): “…there has seen a recent upsurge of interest in studying the time-consistent strategy for the mean–variance problem, see Stroz (1956), Björk and Murgoci (2010), Basak and Chabakauri (2010), Wu (2013), Björk et al. (2014), Björk andMurgoci (2014), Bensoussan et al. (2014) and references therein.”
Robust equilibrium reinsurance-investment strategy for a mean–variance insurer in a model with jumps (2016, background): “For more details, we refer the reader to Björk and Murgoci (2010), Zeng et al. (2013), Li and Li (2013), Björk et al. (2014) and references therein.”
Nash equilibrium strategies for a defined contribution pension management (2015, background): “Björk et al. (2014) consider a continuoustime mean–variance portfolio optimization problem under the assumption that the risk aversion factor depends dynamically on the current wealth.”
Mean-Variance Policy for Discrete-time Cone Constrained Markets: The Consistency in Efficiency and Minimum-Variance Signed Supermartingale Measure (2014, unknown): “As the original dynamic mean-variance formulation is not time consistent, the derived pre-committed dynamic optimal investment policy does not satisfy the principle of optimality and investors have incentive to deviate from such a policy during the investment process in certain circumstances, as rev”