Tutorial for Viscosity Solutions in Optimal Control of Diffusions

Tutorial for Viscosity Solutions in Optimal Control of Diffusions
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扩散优化控制中的粘度解决方案教程

DOI：
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发表时间：
2010
期刊：
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通讯作者：
Jan Palczewski
Jan Palczewski
中科院分区：
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文献类型：
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作者：
G. Aivaliotis;Jan Palczewski

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本教程介绍随机控制问题领域 Hamilton-Jacobi-Bellman 方程/不等式的粘度解理论。对于该理论的面向应用的用户来说，这是一本易于使用的参考书。该演示文稿主要基于 Pham (2009) 《连续时间随机控制和优化与金融应用》一书，但也借鉴了许多其他参考文献。它与现有出版物的不同之处在于注重细节并避免“挥手”。特别是，所有假设都得到了明确的陈述，并且证明以完整的形式呈现。
This tutorial is an introduction to the theory of viscosity solutions of Hamilton-Jacobi-Bellman equations/inequalities in the realm of stochastic control problems. It is an easy to use reference for application-oriented users of this theory. The presentation is based mainly on the book Pham (2009) "Continuous-time Stochastic Control and Optimization with Financial Applications", but borrows from many other references as well. What sets it apart from existing publications is the devotion to details and avoidance of "hand-waving". In particular, all assumptions are clearly stated and proofs are presented in a complete form.