|Abstract: The relative arbitrage portfolio, formulated in Stochastic Portfolio Theory (SPT), outperforms a market portfolio over a given time-horizon with probability one under some conditions on the volatilities in the market, where the optimal relative arbitrage can be characterized by the strict local martingales and the smallest nonnegative continuous solution of a Cauchy problem. In this talk, we consider two regimes: finitely many investors and mean-field, and the corresponding Nash equilibrium of investors who compete with a benchmark determined by the market portfolio and other investors' performance. With the market price of risk processes depending on the market portfolio and total volumes invested, we solve the multi-agent optimization problem under the framework of SPT. This is joint work with Tianjiao Yang.|
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