论文标题
嵌入在单人控制问题中的塞子控制器游戏
Stopper-Controller Games embedded in Single-Player Control Problems
论文作者
论文摘要
2002年，本杰明·乔丹（Benjamin Jourdain）和克劳德·马蒂尼（Claude Martini）发现，对于一类回报功能，美国期权的定价问题可以降低为欧洲期权的定价，以获得适当关联的收益，所有这些都可以在黑色chcholes框架内。 SörenChristensen，Jan Kallsen和Matthias Lenga在2020年最近的一项工作中对这一发现进行了详细的研究。在目前的工作中，我们证明了这种现象可以在更广泛的背景下观察到，甚至在非线性随机过程的设置中也是如此。我们从概率和分析观点分析了这个问题。在经典的情况下，Jourdain和Martini使用这种方法来近似美国的POT选择。现在，更广泛的适用性可能涵盖非线性框架，例如模型不确定性和控制器和稳定游戏。
In 2002, Benjamin Jourdain and Claude Martini discovered that for a class of payoff functions, the pricing problem for American options can be reduced to pricing of European options for an appropriately associated payoff, all within a Black-Scholes framework. This discovery has been investigated in great detail by Sören Christensen, Jan Kallsen and Matthias Lenga in a recent work in 2020. In the present work we prove that this phenomenon can be observed in a wider context, and even holds true in a setup of non-linear stochastic processes. We analyse this problem from both probabilistic and analytic viewpoints. In the classical situation, Jourdain and Martini used this method to approximate prices of American put options. The broader applicability now potentially covers non-linear frameworks such as model uncertainty and controller-and-stopper-games.
