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首页> 外文期刊>Journal of Computational and Applied Mathematics >Semismooth Newton methods with a shooting-like technique for solving a constrained free-boundary HJB equation
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Semismooth Newton methods with a shooting-like technique for solving a constrained free-boundary HJB equation

机译：具有射击型技术的半光滑牛顿方法，用于求解约束自由边界HJB方程

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This paper describes novel numerical methods for solving a constrained free-boundary Hamilton-Jacobi-Bellman (HJB) equation. The equation comes from an optimal dividend problem within financial insurance and has a classical solution under strict assumptions. However the numerical approach is significant since the problem can be classified as a constrained variational inequality with free boundary, for which numerical methods are few. We combine the semismooth Newton method with a shooting-like method to treat the non-smoothness and free boundary of the problem, respectively. We introduce two algorithms, differing only in their treatment of the inequality constraints; the first applies a sweeping method, the second utilizes projected Newton. For the latter, the associated convergence analysis is discussed. In the end, we show that the local convergence rate for this method is at least superlinear. The contribution of this paper is a numerical approach that can be applied to more general free boundary problems with first or second derivative constraints for which analytical solutions are not known. (c) 2021 Elsevier B.V. All rights reserved.
机译：本文描述了求解约束自由边界Hamilton-Jacobi-Bellman（HJB）方程的新数值方法。该方程来源于金融保险中的最优红利问题，在严格假设下有经典解。然而，由于该问题可以归类为一个具有自由边界的约束变分不等式，而数值方法很少，因此数值方法具有重要意义。我们将半光滑牛顿法与类似打靶的方法相结合，分别处理问题的非光滑性和自由边界。我们介绍了两种算法，只在处理不等式约束方面有所不同；第一种方法采用扫掠法，第二种方法采用投影牛顿法。对于后者，讨论了相关的收敛性分析。最后，我们证明了该方法的局部收敛速度至少是超线性的。本文的贡献是一种数值方法，可以应用于更一般的具有一阶或二阶导数约束的自由边界问题，其解析解未知。（c）2021爱思唯尔B.V.保留所有权利。

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