Optimal Growth Strategies in a Stochastic Market Model with Endogenous Prices

We consider a stochastic multiagent market model with endogenous asset prices and find a market strategy which cannot be asymptotically outperformed by a single agent. Such a strategy should distribute its capital among the assets proportionally to the conditional expectations of their discounted relative dividend intensities. The main assumption, under which the results are obtained, is that all agents should be small in the sense that actions of an individual agent do not affect the asset prices. The optimal strategy is found as a solution of a linear backward stochastic differential equation.