Time-Consistent Investment Strategies for Relative Investment Games Under Ambiguity Aversion
With the increasing power of institutional investors, in order to compete for more investment agency business, the competition among institutional investors has become increasingly fierce. This paper studies a non-zero-sum game between two competing institutional investors who adopt mean–variance preferences and account for model uncertainty in order to derive robust optimal portfolios. The ambiguity-averse institutional investors can invest in a financial market with one risk-free bond and one individual stock. The objective of each institutional investor is to maximize the mean–variance utility of his terminal wealth relative to that of his competitor under the worst-case scenario of the alternative measures. By means of stochastic dynamic programming, we obtain closed-form expressions for the robust Nash equilibrium strategies and prove a verification theorem. Numerical simulations are finally presented to examine how model parameters influence the equilibrium strategies and to extract associated economic interpretations.