No abstract

We present turnpike-type results for the risk tolerance function in an incomplete market Itô-diffusion setting under time-monotone forward performance criteria. We show that, contrary to the classical case, the temporal and spatial limits do not coincide. Rather, they depend directly on the left-and right-end of the support of an underlying measure associated with the forward performance criterion. We present examples with discrete and continuous such measures, and discuss the asymptotic behavior of the risk tolerance for each case. * This work was presented at seminars and workshops at ETH, King's College, Princeton, Oxford and Columbia University. The authors would like to thank the participants for fruitful comments and suggestions.

No abstract

No abstract

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, 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, thus also extending 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 the incomplete market cases.

No abstract

No abstract