 This paper analyzes the market behavior and optimal investment strategies to attain relative arbitrage both in the N investors and mean field regimes  . An investor competes with a benchmark of market and peer investors, expecting to outperform the benchmark and minimizing the \%proportion of initial capital. With market price of risk processes depending on the stock market and investors respectively, the minimal initial capital required is the optimal cost in the N-player games and mean field games. It can be characterized as the smallest nonnegative continuous solution of a Cauchy problem. The measure flow of wealth appears in the cost, while the joint flow of wealth and strategy is in state processes. We modify the extended mean field game with common noise and its notion of the uniqueness of Nash equilibrium . There is a unique equilibrium in N-player games and mean field games with mild conditions on the equity market.
The relative arbitrage portfolio, formulated in Stochastic Portfolio Theory (SPT), outperforms a benchmark portfolio over a given time-horizon with probability one. This paper analyzes the market behavior and optimal investment strategies to attain relative arbitrage both in the N investors and mean field regimes under some market conditions . An investor competes with a benchmark of market and peer investors, expecting to outperform the benchmark and minimizing the initial capital. With market price of risk processes depending on the market portfolio and investors, we develop a systematic way to solve multi-agent optimization problem within SPT's framework. The objective can be characterized by the smallest nonnegative continuous solution of a Cauchy problem. By a modification in the structure of the extended mean field game with common noise and its notion of the uniqueness of Nash equilibrium , we show a unique equilibrium in N-player games and mean field games with mild conditions on the equity market.
A
The relative arbitrage portfolio, formulated in Stochastic Portfolio Theory (SPT), outperforms a benchmark portfolio over a given time-horizon with probability one.
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under some market conditions
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stock market and investors respectively, the minimal initial capital required is the optimal cost in the N-player games and mean field games. It
market portfolio and investors, we develop a systematic way to solve multi-agent optimization problem within SPT's framework. The objective
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as
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The measure flow of wealth appears in the cost, while the joint flow of wealth and strategy is in state processes. We modify
By a modification in the structure of
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. There is
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