Optimal Stopping Under Ambiguity
Optimal Stopping Under Ambiguity
复制标题
歧义下的最佳停止
DOI：
--
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
F. Riedel
中科院分区：
文献类型：
--
作者：
F. Riedel
我们考虑具有多个先验的模糊厌恶决策者的最优停止问题。一般来说，逆向归纳法失败了。然而，如果类的先验是时间一致的，我们建立一个推广的经典理论的最佳停止。为此，我们发展的第一步，多个先验的鞅理论。我们定义了极大极小（上）鞅，提供了一个Doob-Meyer分解，并刻画了极大极小鞅。这使我们能够将标准的逆向归纳程序扩展到模糊的、时间一致的偏好。价值函数是极小极大上鞅的最小过程，并且支配支付过程。当当前收益等于价值函数时，停止是最优的。接下来，我们研究无限视界的情况。我们发现，价值过程满足相同的向后递归（贝尔曼方程）在有限的地平线的情况下。有限时域解收敛到无限时域解。最后，我们完全刻画了二叉树中时间一致多重先验集。我们解决了两类例子：所谓的独立和不可区分的情况下（停车问题）和美式期权的情况下（考克斯-罗斯-鲁宾斯坦模型）。
We consider optimal stopping problems for ambiguity averse decision makers with multiple priors. In general, backward induction fails. If, however, the class of priors is time-consistent, we establish a generalization of the classical theory of optimal stopping. To this end, we develop first steps of a martingale theory for multiple priors. We define minimax (super)martingales, provide a Doob-Meyer decomposition, and characterize minimax martingales. This allows us to extend the standard backward induction procedure to ambiguous, time-consistent preferences. The value function is the smallest process that is a minimax supermartingale and dominates the payoff process. It is optimal to stop when the current payoff is equal to the value function. Moving on, we study the infinite horizon case. We show that the value process satisfies the same backward recursion (Bellman equation) as in the finite horizon case. The finite horizon solutions converge to the infinite horizon solution. Finally, we characterize completely the set of time-consistent multiple priors in the binomial tree. We solve two classes of examples: the so-called independent and indistinguishable case (the parking problem) and the case of American Options (Cox-Ross-Rubinstein model).