英文标题：
《Pricing insurance drawdown-type contracts with underlying L\\\'evy assets》
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作者：
Zbigniew Palmowski and Joanna Tumilewicz
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最新提交年份：
2017
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英文摘要：
In this paper we consider some insurance policies related to drawdown and drawup events of log-returns for an underlying asset modeled by a spectrally negative geometric L\\\'evy process. We consider four contracts, three of which were introduced in Zhang et al. (2013) for a geometric Brownian motion. The first one is an insurance contract where the protection buyer pays a constant premium until the drawdown of fixed size of log-returns occurs. In return he/she receives a certain insured amount at the drawdown epoch. The next insurance contract provides protection from any specified drawdown with a drawup contingency. This contract expires early if a certain fixed drawup event occurs prior to the fixed drawdown. The last two contracts are extensions of the previous ones by an additional cancellation feature which allows the investor to terminate the contract earlier. We focus on two problems: calculating the fair premium $p$ for the basic contracts and identifying the optimal stopping rule for the policies with the cancellation feature. To do this we solve some two-sided exit problems related to drawdown and drawup of spectrally negative L\\\'evy processes, which is of independent mathematical interest. We also heavily rely on the theory of optimal stopping.
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中文摘要：
在本文中，我们考虑了一些与对数收益率的提取和提取事件相关的保险政策，这些事件是由光谱负几何L拞evy过程建模的基础资产的。我们考虑了四个契约，其中三个是在Zhang et al.（2013）中针对几何布朗运动引入的。第一种是保险合同，其中保护买方支付固定保费，直到提取固定大小的原木退货。作为回报，他/她在提款期收到一定的保险金额。下一份保险合同提供了针对任何指定支取的保护，包括支取意外开支。如果在固定支取之前发生某个固定支取事件，则本合同提前到期。最后两份合同是前两份合同的扩展，增加了一项取消功能，允许投资者提前终止合同。我们关注两个问题：计算基本合约的公平保费$p$，以及确定具有取消功能的保单的最优停止规则。为了做到这一点，我们解决了一些双边退出问题，这些问题与光谱负L拞evy过程的下降和上升有关，这是一个独立的数学问题。我们还严重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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