Competition in Fund Management and Forward Relative Performance Criteria

SIAM Journal on Financial Mathematics, Volume 13, Issue 4, Page 1271-1301, December 2022.
In an Itô-diffusion market, two fund managers trade under relative performance concerns. For both the asset specialization and diversification settings, we analyze the passive and competitive cases. We measure the performance of the managers' strategies via forward relative performance criteria, leading to the respective notions of forward best-response criterion and forward Nash equilibrium. The motivation to develop such criteria comes from the need to relax various crucial, but quite stringent for this problem, existing assumptions, such as the a priori choices of both the market model and the investment horizon, the commonality of the latter for both managers, as well as the full a priori knowledge of the competitor's policies for the best-response case. We focus on locally riskless criteria and deduce the random forward equations. We solve the CRRA cases and thus also extend the related results in the classical setting. An important by-product of the work herein is the development of forward performance criteria for investment problems in Itô-diffusion markets under the presence of correlated random endowment process for both the perfectly and incomplete market cases.