Before revision:  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.
After revision:  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 as the smallest nonnegative continuous solution of a Cauchy problem.