On an asymptotic viscosity solution property of solutions of discrete Hamilton-Jacobi-Bellman equations
On an asymptotic viscosity solution property of solutions of discrete Hamilton-Jacobi-Bellman equations
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离散Hamilton-Jacobi-Bellman方程解的渐近粘性解性质
DOI：
10.1007/s40314-017-0549-3
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发表时间：
2018
影响因子：
2.6
通讯作者：
Naohiro Yoshida
中科院分区：
文献类型：
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作者：
Naohiro Yoshida
本文证明了随机游动模型中离散Hamilton-Jacobi-Bellman（dHJB）方程解的一个真极限成为连续时间几何布朗模型中Hamilton-Jacobi-Bellman（HJB）变分不等式的粘性解.利用HJB变分不等式分析金融数学中的奇异随机控制问题。利用我们的结果，借助于dHJB方程，我们可以得到HJB变分不等式的粘性解，这些解通常与奇异随机控制问题的值函数一致.
In this paper, we show that a proper limit of solutions of discrete Hamilton–Jacobi–Bellman (dHJB) equations in a random walk model becomes a viscosity solution of a Hamilton–Jacobi–Bellman (HJB) variational inequality in a continuous-time geometric Brownian model. HJB variational inequalities are used to analyze singular stochastic control problems in mathematical finance. By our result, with the help of dHJB equations, we can obtain viscosity solutions of HJB variational inequalities which are usually identified with the value functions of the singular stochastic control problems.