Optimal portfolio selection of many players and dynamic portfolio allocation with goals-based wealth management

Abstract

either all agents have Constant Absolute Risk Aversion (CARA) risk preferences or all agents have Constant Relative Risk Aversion (CRRA) risk preferences for their investment optimization problem. For each case, we show that the forward Nash equilibrium and the mean field equilibrium exist for the n-agent game and the corresponding mean field stochastic optimal control problem, respectively. We conclude that our optimal portfolio formulas extend the corresponding results of the market model with constant coefficients. Also, in this thesis, we extend the previous research on dynamic portfolio allocation with goals-based wealth management in two directions. Firstly, we consider the case that an investor has more than one goal with different investment horizons. Secondly, we consider the case where there is a risk-free asset in the market. For each case, the results are obtained through simulation and analyzed.

Researches on optimal portfolio selection problem and dynamic portfolio allocation have been actively conducted. In this thesis, we study the optimal portfolio selection problem under relative performance criteria in the market model with random coefficients from the perspective of many players game theory. We focus on two cases