Nonlinear PDE Approach to Time-Inconsistent Optimal Stopping
Nonlinear PDE Approach to Time-Inconsistent Optimal Stopping
复制标题
时间不一致最优停止的非线性 PDE 方法
DOI：
10.1137/15m1047064
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Christopher W. Miller
中科院分区：
文献类型：
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作者：
Christopher W. Miller
我们提出了一种新的方法来解决一类时间不一致的最优停止问题，将其归结为一族标准随机最优控制问题。特别是，我们转换为一个标准的随机控制问题，一个额外的状态变量的辅助值函数的优化目标中的期望停止时间的非线性函数的最优停止问题。这种方法不同于以前的文献，主要采用拉格朗日乘子方法或依赖于精确解。相反，我们的辅助值函数的唯一粘性解的非线性椭圆型偏微分方程，满足一定的增长约束和调查的基本规律性。我们证明了辅助值函数的额外的正则性假设下的最优停时的建设。最后，我们将讨论扩展到更一般的动力学和时间不一致性，以及潜在的连接退化蒙赫-安培方程。
We present a novel method for solving a class of time-inconsistent optimal stopping problems by reducing them to a family of standard stochastic optimal control problems. In particular, we convert an optimal stopping problem with a non-linear function of the expected stopping time in the objective into optimization over an auxiliary value function for a standard stochastic control problem with an additional state variable. This approach differs from the previous literature which primarily employs Lagrange multiplier methods or relies on exact solutions. In contrast, we characterize the auxiliary value function as the unique viscosity solution of a non-linear elliptic PDE which satisfies certain growth constraints and investigate basic regularity properties. We demonstrate the construction of an optimal stopping time under additional regularity assumptions on the auxiliary value function. Finally, we discuss extensions to more general dynamics and time-inconsistencies, as well as potential connections to degenerate Monge-Ampere equations.
DOI：
10.1137/16m1058492
发表时间：
2015-12
期刊：
SIAM J. Control. Optim.
影响因子：
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作者：
Christopher W. Miller;Insoon Yang
通讯作者：
Christopher W. Miller;Insoon Yang