具有一般保险和惩罚函数的Lévy型提取-提取合同的公平估值
Fair valuation of Lévy-type drawdown-drawup contracts with general insured and penalty functions
摘要：
在本文中，我们分析了一些股票挂钩的合同，涉及提取和提取事件的基础上的资产由一个几何谱负莱维过程。回撤和回撤分别是指资产价格的历史最高值和历史最低值与其当前价值之间的差异。我们考虑四个合同。在第一个合同中，保护买方以恒定的强度$p$支付保险费，直到发生固定规模的缩编。作为回报，他/她在提款时期收到一定的保险金额，这取决于当时的提款水平。其次，如果在定额提取之前发生某个定额提取事件，则保险合同可能会提前到期。最后两份合同是前两份合同的延伸，但具有额外的可撤销特征，允许投资者提前终止合同。在这些情况下，提前停止的费用取决于停止时期的水位下降水平。本文主要研究两个问题：基本合约的公平保费$p$的计算和具有可撤销特征的保单的最优停时的求解。为此，我们使用Lévy过程的波动理论，并依赖于最优停时理论。
英文摘要：
In this paper, we analyse some equity-linked contracts that are related to drawdown and drawup events based on assets governed by a geometric spectrally negative Lévy process. Drawdown and drawup refer to the differences between the historical maximum and minimum of the asset price and its current value, respectively. We consider four contracts. In the first contract, a protection buyer pays a premium with a constant intensity $p$ until the drawdown of fixed size occurs. In return, he/she receives a certain insured amount at the drawdown epoch, which depends on the drawdown level at that moment. Next, the insurance contract may expire earlier if a certain fixed drawup event occurs prior to the fixed drawdown. The last two contracts are extensions of the previous ones but with an additional cancellable feature that allows the investor to terminate the contracts earlier. In these cases, a fee for early stopping depends on the drawdown level at the stopping epoch. In this work, we focus on two problems: calculating the fair premium $p$ for basic contracts and finding the optimal stopping rule for the polices with a cancellable feature. To do this, we use a fluctuation theory of Lévy processes and rely on a theory of optimal stopping.
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