SIAM Journal on Control and Optimization, Volume 58, Issue 2, Page 866-894, January 2020.
In this paper we propose a unified utility deviation-risk model which covers both utility maximization and mean-variance analysis as special cases. We derive the time-consistent Hamilton--Jacobi--Bellman (HJB) equation for the equilibrium value function and significantly reduce the number of state variables, which makes the HJB equation derived in this paper much easier to solve than the extended HJB equation in the literature. We illustrate the usefulness of the time-consistent HJB equation with several examples which recover the known results in the literature and go beyond, including a mean-variance model with stochastic volatility dependent risk aversion, a utility deviation-risk model with state dependent risk aversion and control constraint, and a constrained portfolio selection model. The numerical and statistical tests show that the utility and deviation-risk have a significant impact on the equilibrium control strategy and the distribution of the terminal wealth.

中文翻译：

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约束效用偏差风险优化和时间一致性HJB方程

SIAM控制与优化杂志，第58卷，第2期，第866-894页，2020年1月。
在本文中，我们提出了一个统一的效用偏差风险模型，其中涵盖了效用最大化和均方差分析这两种特殊情况。我们为平衡值函数导出了时间一致的Hamilton-Jacobi-Bellman（HJB）方程，并显着减少了状态变量的数量，这使得本文中导出的HJB方程比扩展的HJB方程更容易求解。文献。我们用几个例子来说明时间一致的HJB方程的有效性，这些例子可以恢复文献中的已知结果，并且超出范围，包括具有随机波动率依赖的风险规避的均方差模型，具有状态依赖的风险规避的效用偏差风险模型和控制约束，以及受约束的投资组合选择模型。