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摘要翻译：
我们考虑一个金融契约，它提供由累积收益过程的终端价值给出的单一现金流。例如，在确定最优保险索赔准备金保单和再保险合同的定价中，这种资产及其相关衍生工具的建模和定价问题是很重要的。在保险环境中，索赔总额起到累积收益的作用，终端现金流量代表给定会计期间应付索赔的总额。当我们考虑一个信贷投资组合中损失的累积，并对一个在给定时间间隔内支付的金额等于损失总额的合同进行估价时，就会出现一个类似的例子。得到了值过程的显式表达式。在累积收益过程中确定Arrow-Debreu证券的价格，并用它来获得欧式期权价格与资产价值的闭式表达式。所得结果利用了伽玛桥过程的各种显著性质，并适用于各种基于累积收益过程的金融产品，如总索赔、信贷组合损失、固定福利养老金计划、排放和降雨。
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英文标题：
《Dam Rain and Cumulative Gain》
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作者：
Dorje C. Brody, Lane P. Hughston, Andrea Macrina
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最新提交年份：
2007
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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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英文摘要：
We consider a financial contract that delivers a single cash flow given by the terminal value of a cumulative gains process. The problem of modelling and pricing such an asset and associated derivatives is important, for example, in the determination of optimal insurance claims reserve policies, and in the pricing of reinsurance contracts. In the insurance setting, the aggregate claims play the role of the cumulative gains, and the terminal cash flow represents the totality of the claims payable for the given accounting period. A similar example arises when we consider the accumulation of losses in a credit portfolio, and value a contract that pays an amount equal to the totality of the losses over a given time interval. An explicit expression for the value process is obtained. The price of an Arrow-Debreu security on the cumulative gains process is determined, and is used to obtain a closed-form expression for the price of a European-style option on the value of the asset. The results obtained make use of various remarkable properties of the gamma bridge process, and are applicable to a wide variety of financial products based on cumulative gains processes such as aggregate claims, credit portfolio losses, defined-benefit pension schemes, emissions, and rainfall.
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PDF链接：
https://arxiv.org/pdf/0710.2775
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