The aim of this study is to explore the behavior of perpetual game put options, also known as cancellable puts. Their main characteristic is the opportunity of the buyer and the seller to exercise prematurely. If the seller decides to terminate the option, he obliges to pay a penalty amount above the normal option fee. We include also a discount factor that provides an advantage for earlier option exercising. We obtain the optimal moments for both participants to end the option promptly. This allows us to turn the option pricing problem to a first exit problem. We base our examination on financial instruments with random maturities. These instruments permit one of the partakers to maximize his expected future profit.

这项研究的目的是探讨永久博弈认沽期权（也称为可取消认沽期权）的行为。它们的主要特征是买卖双方过早行使的机会。如果卖方决定终止期权，则他有义务支付高于正常期权费的罚款。我们还包括一个折现因子，为较早的期权行使提供了优势。我们为双方参与者获得最佳时机，以迅速结束选择权。这使我们可以将期权定价问题转变为首次退出问题。我们的检查基于具有随机期限的金融工具。这些工具使其中一名合伙人能够最大化其预期的未来利润。