英文标题：
《Transformation Method for Solving Hamilton-Jacobi-Bellman Equation for
Constrained Dynamic Stochastic Optimal Allocation Problem》
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作者：
Sona Kilianova and Daniel Sevcovic
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最新提交年份：
2013
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英文摘要：
In this paper we propose and analyze a method based on the Riccati transformation for solving the evolutionary Hamilton-Jacobi-Bellman equation arising from the stochastic dynamic optimal allocation problem. We show how the fully nonlinear Hamilton-Jacobi-Bellman equation can be transformed into a quasi-linear parabolic equation whose diffusion function is obtained as the value function of certain parametric convex optimization problem. Although the diffusion function need not be sufficiently smooth, we are able to prove existence, uniqueness and derive useful bounds of classical H\\\"older smooth solutions. We furthermore construct a fully implicit iterative numerical scheme based on finite volume approximation of the governing equation. A numerical solution is compared to a semi-explicit traveling wave solution by means of the convergence ratio of the method. We compute optimal strategies for a portfolio investment problem motivated by the German DAX 30 Index as an example of application of the method.
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中文摘要：
本文提出并分析了一种基于Riccati变换的求解随机动态最优分配问题演化Hamilton-Jacobi-Bellman方程的方法。我们展示了如何将完全非线性的Hamilton-Jacobi-Bellman方程转化为一个拟线性抛物方程，其扩散函数作为某个参数凸优化问题的值函数。虽然扩散函数不需要足够光滑，但我们能够证明它的存在，经典H的唯一性及其有用界的推导\\“旧的光滑解。我们进一步构造了一个基于控制方程有限体积近似的全隐式迭代数值格式。通过该方法的收敛率，将数值解与半显式行波解进行了比较。我们以德国DAX 30指数为例，计算了一个投资组合问题的最优策略方法的应用。
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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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