神经最优停止边界

Optimal multiple stopping with random waiting times

In the standard models for optimal multiple stopping problems it is assumed that between two exercises there is always a time period of deterministic length $δ$, the so called refraction period. This prevents the optimal exercise times from bunching up together on top of the optimal stopping time for the one-exercise case. In this article we generalize the standard model by considering random refraction times. We develop the theory and reduce the problem to a sequence of ordinary stopping problems thus extending the results for deterministic times. This requires an extension of the underlying …

Optimal Stopping for Non-linear Expectations

We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards.

Regularity of the Optimal Stopping Problem for Jump Diffusions

The value function of an optimal stopping problem for jump diffusions is known to be a generalized solution of a variational inequality. Assuming that the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the Lévy measure, this paper shows that the value function of this optimal stopping problem on an unbounded domain with finite/infinite variation jumps is in $W^{2,1}_{p, loc}$ with $p\in(1, \infty)$. As a consequence, the smooth-fit property holds.

On the optimal exercise boundaries of swing put options

We use probabilistic methods to characterise time dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications we consider a payoff of immediate stopping of "put" type and the underlying dynamics follows a geometric Brownian motion. The optimal stopping region relative to each optimal stopping time is described in terms of two boundaries which are continuous, monotonic functions of time and uniquely solve a system of coupled integral equations of Volterra-type. Finally we provide a formula for the value function o…

A Class of Solvable Optimal Stopping Problems of Spectrally Negative Jump Diffusions

We consider the optimal stopping of a class of spectrally negative jump diffusions. We state a set of conditions under which the value is shown to have a representation in terms of an ordinary nonlinear programming problem. We establish a connection between the considered problem and a stopping problem of an associated continuous diffusion process and demonstrate how this connection may be applied for characterizing the stopping policy and its value. We also establish a set of typically satisfied conditions under which increased volatility as well as higher jump-intensity decelerates rational …

通过深度强化学习的连续时间最优停止

Continuous-time Optimal Stopping through Deep Reinforcement Learning

提出CARLOS算法，利用聚合深度神经网络学习任意精细时间分辨率下的停止规则，通过渐进式时间网格细化和自适应采样，逼近美式期权价格上界。