论文标题
在市场模型的相对绩效标准下，选择许多玩家的最佳投资组合与随机系数
Optimal portfolio selection of many players under relative performance criteria in the market model with random coefficients
论文作者
论文摘要
从许多玩家游戏理论的角度来看，我们在市场模型的相对绩效标准下研究了最佳的投资组合选择问题。我们考虑五个随机系数，这些系数由三个市场参数组成，这些参数用于风险资产价格建模和两个与风险态度和相对绩效影响有关的偏好参数。我们专注于两种情况；所有代理都有恒定的绝对风险避免（CARA）风险偏好，或者所有代理都在其投资优化问题上都具有恒定的相对风险避免（CRRA）风险偏好。对于每种情况，我们都表明，N-Agent Game和相应的平均场随机最佳控制问题都存在正向NASH平衡和平均场平衡。为了将N代理游戏扩展到玩家游戏的连续性，我们引入了一个依赖度量的前瞻性相对性能过程，并对McKean-Vlasov类型的受控动力进行了优化。我们得出的结论是，我们的最佳投资组合公式以恒定系数扩展了市场模型的相应结果。
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 consider five random coefficients which consist of three market parameters which are used in the risky asset price modeling and two preference parameters which are related to risk attitude and impact of relative performance. We focus on two cases; 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. To extend the n-agent game to the continuum of players game, we introduce a measure dependent forward relative performance process and apply an optimization over controlled dynamics of McKean-Vlasov type. We conclude that our optimal portfolio formulas extend the corresponding results of the market model with constant coefficients.
