摘要翻译：
本文给出了离散时间利率模型的一个公理格式。我们采用了定价核心方法，它建立在无套利属性中，并提供了与均衡经济学的联系。我们要求定价核与一对公理一致，一个公理给出支付股利资产的时间间关系，另一个公理确保货币市场资产的存在。我们证明了正收益资产的存在意味着一个可预见的货币市场账户的存在。导出了有限责任资产价格过程的一般表达式。这个表达式包括两个术语，一个是股利流的折现风险调整值，另一个是留存收益的特征。后者的消失由横截性条件给出。我们证明（在假定的公理下），在没有永久留存收益的有限责任资产的情况下，价格过程是由一对潜力的比率给出的。提供了离散时间模型的明确例子。
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英文标题：
《Discrete-Time Interest Rate Modelling》
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作者：
Lane P. Hughston and Andrea Macrina
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最新提交年份：
2009
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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：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
  This paper presents an axiomatic scheme for interest rate models in discrete time. We take a pricing kernel approach, which builds in the arbitrage-free property and provides a link to equilibrium economics. We require that the pricing kernel be consistent with a pair of axioms, one giving the inter-temporal relations for dividend-paying assets, and the other ensuring the existence of a money-market asset. We show that the existence of a positive-return asset implies the existence of a previsible money-market account. A general expression for the price process of a limited-liability asset is derived. This expression includes two terms, one being the discounted risk-adjusted value of the dividend stream, the other characterising retained earnings. The vanishing of the latter is given by a transversality condition. We show (under the assumed axioms) that, in the case of a limited-liability asset with no permanently-retained earnings, the price process is given by the ratio of a pair of potentials. Explicit examples of discrete-time models are provided.
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PDF链接：
https://arxiv.org/pdf/0911.0750