摘要翻译:
本文证明了一类效用函数不一定可微或严格凹的约束问题的HJB方程存在光滑的经典解。当容许控制满足可积条件或在其区域的闭包上连续时,该值函数是光滑的。其核心思想是研究对偶控制问题和对偶HJB方程。构造了对偶HJB方程的光滑严格凸解,并证明了它的共轭函数是满足终端和边界条件的原HJB方程的光滑严格凹解。
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英文标题:
《Smooth Value Functions for a Class of Nonsmooth Utility Maximization
Problems》
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作者:
Baojun Bian, Sheng Miao, Harry Zheng
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最新提交年份:
2010
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分类信息:
一级分类:Quantitative Finance 数量金融学
二级分类:Computational Finance 计算金融学
分类描述:Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法,包括蒙特卡罗,偏微分方程,格子和其他数值方法,并应用于金融建模
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英文摘要:
In this paper we prove that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave. The value function is smooth if admissible controls satisfy an integrability condition or if it is continuous on the closure of its domain. The key idea is to work on the dual control problem and the dual HJB equation. We construct a smooth, strictly convex solution to the dual HJB equation and show that its conjugate function is a smooth, strictly concave solution to the primal HJB equation satisfying the terminal and boundary conditions.
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PDF链接:
https://arxiv.org/pdf/1005.3956