Scholarlink

<p>In this paper, we study the optimal investment problem for competitive agents with stochastic income under constant absolute risk aversion (CARA) relative performance, in both the finite population game and the mean field game (MFG) frameworks. The agents’ stochastic income processes are partially correlated with risky assets but cannot be fully hedged. At the same time, an insurance mechanism is considered to manage residual income risks. By solving Hamilton-Jacobi-Bellman (HJB) equations and fixed-point problems, we derive time-dependent Nash equilibrium strategies for both the investment portfolios and income insurance in the finite population game and the corresponding MFG. We also conduct numerical analysis to validate our theoretical results, demonstrating the convergence of the finite population equilibrium to the mean field equilibrium (MFE) as the number of agents approaches infinity. More interestingly, our numerical simulations further reveal the economic significance of various parameters: a higher competition weight can increase risky asset holdings and income risk retention ratios, while increased income volatility reduces them.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Optimal Investment for Agents with Unhedgeable Stochastic Income in Competitive Games

  • 期刊论文

  • 发表日期：

    2026年6月1日

查看全文
  • Li Wei,
  • Yaoyi Wei,
  • Ming Zhou

摘要

In this paper, we study the optimal investment problem for competitive agents with stochastic income under constant absolute risk aversion (CARA) relative performance, in both the finite population game and the mean field game (MFG) frameworks. The agents’ stochastic income processes are partially correlated with risky assets but cannot be fully hedged. At the same time, an insurance mechanism is considered to manage residual income risks. By solving Hamilton-Jacobi-Bellman (HJB) equations and fixed-point problems, we derive time-dependent Nash equilibrium strategies for both the investment portfolios and income insurance in the finite population game and the corresponding MFG. We also conduct numerical analysis to validate our theoretical results, demonstrating the convergence of the finite population equilibrium to the mean field equilibrium (MFE) as the number of agents approaches infinity. More interestingly, our numerical simulations further reveal the economic significance of various parameters: a higher competition weight can increase risky asset holdings and income risk retention ratios, while increased income volatility reduces them.