英文标题：
《Fair valuation of L\\\'evy-type drawdown-drawup contracts with general
insured and penalty functions》
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作者：
Zbigniew Palmowski and Joanna Tumilewicz
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最新提交年份：
2018
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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 L\\\'evy 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 L\\\'evy processes and rely on a theory of optimal stopping.
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中文摘要：
在本文中，我们分析了一些与提取和提取事件相关的股票挂钩合同，这些合同基于受几何频谱负L拞evy过程控制的资产。提取和提取分别指资产价格的历史最大值和最小值与其当前价值之间的差额。我们考虑四份合同。在第一份合同中，保护买方以固定的强度支付保费$p$，直到出现固定规模的提款。作为回报，他/她在提款期收到一定的保险金额，这取决于当时的提款水平。其次，如果某个固定支取事件发生在固定支取之前，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，但有一个额外的可取消功能，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提款水平。在这项工作中，我们关注两个问题：计算基本合同的公平保费$p$，以及找到具有可取消特征的策略的最优停止规则。为此，我们使用了列维过程的波动理论，并依赖于最优停止理论。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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