英文标题：
《Positive Eigenfunctions of Markovian Pricing Operators:
  Hansen-Scheinkman Factorization, Ross Recovery and Long-Term Pricing》
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作者：
Likuan Qin and Vadim Linetsky
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最新提交年份：
2015
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英文摘要：
  This paper develops a spectral theory of Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space (Borel right process (BRP)) and the stochastic discount factor (SDF) is a positive semimartingale multiplicative functional of X. A key result is the uniqueness theorem for a positive eigenfunction of the pricing operator such that X is recurrent under a new probability measure associated with this eigenfunction (recurrent eigenfunction). As economic applications, we prove uniqueness of the Hansen and Scheinkman (2009) factorization of the Markovian SDF corresponding to the recurrent eigenfunction, extend the Recovery Theorem of Ross (2015) from discrete time, finite state irreducible Markov chains to recurrent BRPs, and obtain the long maturity asymptotics of the pricing operator. When an asset pricing model is specified by given risk-neutral probabilities together with a short rate function of the Markovian state, we give sufficient conditions for existence of a recurrent eigenfunction and provide explicit examples in a number of important financial models, including affine and quadratic diffusion models and an affine model with jumps. These examples show that the recurrence assumption, in addition to fixing uniqueness, rules out unstable economic dynamics, such as the short rate asymptotically going to infinity or to a zero lower bound trap without possibility of escaping.
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中文摘要：
本文发展了马尔可夫资产定价模型的谱理论，其中潜在的经济不确定性遵循具有一般状态空间的连续时间马尔可夫过程X（Borel right process（BRP）），随机贴现因子（SDF）是X的正半鞅乘性泛函。一个关键结果是定价的正特征函数的唯一性定理算子，使得X在与该特征函数（递归特征函数）相关的新概率测度下是递归的。作为经济应用，我们证明了与递归特征函数对应的马尔可夫SDF的Hansen和Scheinkman（2009）因子分解的唯一性，将Ross（2015）的恢复定理从离散时间、有限状态不可约马尔可夫链推广到了递归BRP，并获得了定价算子的长成熟渐近性。当一个资产定价模型由给定的风险中性概率和马尔可夫状态的短利率函数指定时，我们给出了一个循环特征函数存在的充分条件，并在一些重要的金融模型中给出了明确的例子，包括仿射和二次扩散模型以及带跳跃的仿射模型。这些例子表明，除了固定唯一性外，递归假设还排除了不稳定的经济动态，例如短期利率渐近地趋于无穷大或零下限陷阱，而不存在逃脱的可能性。
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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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