发帖
雷达卡
英文标题：
《No-Arbitrage Prices of Cash Flows and Forward Contracts as Choquet
Representations》
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作者：
Tom Fischer
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最新提交年份：
2015
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英文摘要：
In a market of deterministic cash flows, given as an additive, symmetric relation of exchangeability on the finite signed Borel measures on the non-negative real time axis, it is shown that the only arbitrage-free price functional that fulfills some additional mild requirements is the integral of the unit zero-coupon bond prices with respect to the payment measures. For probability measures, this is a Choquet representation, where the Dirac measures, as unit zero-coupon bonds, are the extreme points. Dropping one of the requirements, the Lebesgue decomposition is used to construct counterexamples, where the Choquet price formula does not hold despite of an arbitrage-free market model. The concept is then extended to deterministic streams of assets and currencies in general, yielding a valuation principle for forward markets. Under mild assumptions, it is shown that a foreign cash flow\'s worth in local currency is identical to the value of the cash flow in local currency for which the Radon-Nikodym derivative with respect to the foreign cash flow is the forward FX rate.
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中文摘要：
在确定性现金流市场中，给出了非负实时轴上有限符号Borel测度上可交换性的加性对称关系，证明了满足一些额外温和要求的唯一无套利价格函数是单位零息票债券价格相对于支付测度的积分。对于概率度量，这是Choquet表示，其中Dirac度量，作为单位零息票债券，是极值点。除去其中一项要求，Lebesgue分解用于构造反例，其中Choquet价格公式不适用于无套利市场模型。然后，该概念被扩展到一般的确定性资产和货币流，从而产生远期市场的估值原则。在温和的假设下，可以看出，外币现金流的本币价值与以本币表示的现金流价值相同，而与外币现金流相关的Radon Nikodym衍生工具是远期汇率。
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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