英文标题：
《Dynamic intertemporal utility optimization by means of Riccati
transformation of Hamilton-Jacobi Bellman equation》
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作者：
Sona Kilianova, Daniel Sevcovic
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最新提交年份：
2019
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英文摘要：
In this paper we investigate a dynamic stochastic portfolio optimization problem involving both the expected terminal utility and intertemporal utility maximization. We solve the problem by means of a solution to a fully nonlinear evolutionary Hamilton-Jacobi-Bellman (HJB) equation. We propose the so-called Riccati method for transformation of the fully nonlinear HJB equation into a quasi-linear parabolic equation with non-local terms involving the intertemporal utility function. As a numerical method we propose a semi-implicit scheme in time based on a finite volume approximation in the spatial variable. By analyzing an explicit traveling wave solution we show that the numerical method is of the second experimental order of convergence. As a practical application we compute optimal strategies for a portfolio investment problem motivated by market financial data of German DAX 30 Index and show the effect of considering intertemporal utility on optimal portfolio selection.
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中文摘要：
本文研究了一个同时考虑期望终端效用和跨期效用最大化的动态随机投资组合优化问题。我们通过求解一个完全非线性的演化Hamilton-Jacobi-Bellman（HJB）方程来解决这个问题。我们提出了所谓的Riccati方法，将完全非线性的HJB方程转化为包含跨期效用函数的非局部项的拟线性抛物方程。作为一种数值方法，我们提出了一种基于空间变量有限体积近似的半隐式时间格式。通过分析一个显式行波解，我们表明该数值方法具有二阶实验收敛性。作为一个实际应用，我们计算了一个由德国DAX 30指数的市场金融数据驱动的组合投资问题的最优策略，并展示了考虑跨期效用对最优组合选择的影响。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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