The Term Structure of Interest Rates as a Random Field: a Stochastic Integration Approach
The Term Structure of Interest Rates as a Random Field: a Stochastic Integration Approach
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作为随机场的利率期限结构：随机积分方法
DOI：
10.1142/9789812702852_0002
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
M. Donno
中科院分区：
文献类型：
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作者：
M. Donno
摘要：在远期利率呈维纳表演变的情况下，我们研究了零息债券的期限结构。我们引入了关于具有连续函数集合中的值的连续半鞅的随机积分的定义，并表征了零息债券的动态。我们还定义了广义策略的概念，以承认投资连续体债券的（理论上）可能性。最后我们研究了这种情况下终端财富效用最大化的问题，并推导出“共同基金”定理。
AbstractWe investigate the term structure of zero coupon bonds, in the case where the forward rate evolves as a Wiener sheet. We introduce a definition of stochastic integral with respect to a continuous semimartingale with values in the set of continuous functions and characterize the dynamics of the zero coupon bonds. We also define a notion of generalized strategy, in order to admit the (theoretical) possibility of investing in a continuum of bonds. Finally we study the problem of utility maximization from terminal wealth in this setting and deduce a "mutual fund" theorem.