In this paper, we investigate an optimal investment problem under two value-at-risk (VaR) constraints faced by a defined contribution (DC) pension fund manager. We apply a concavification technique and a Lagrange dual method to solve the problem and derive the closed-form representations of the optimal wealth and portfolio processes in terms of the state price density. Theoretical and numerical results show that the two VaR constraints can significantly impact the distribution of the optimal terminal wealth.

中文翻译：

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具有两个VaR约束的DC养老金计划的最优投资

在本文中，我们研究了定义缴费型（DC）养老基金经理面临的两个风险价值（VaR）约束下的最优投资问题。我们应用凹化技术和Lagrange对偶方法来解决问题，并根据状态价格密度得出最优财富和投资组合过程的闭式表示。理论和数值结果表明，这两个VaR约束可以显着影响最优终端财富的分布。