Nonparametric Identification of Positive Eigenfunctions

Christensen, Timothy

doi:10.1017/s0266466614000668

Cited by 17 publications

(9 citation statements)

References 35 publications

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“…Qin, Linetsky, and Nie (2016) further showed that, under L, the term structure of bond Sharpe ratios for a sufficiently small holding period generally has an increasing shape in the bond maturity T , with the long bond achieving the maximal instantaneous Sharpe ratio under L (the Hansen and Jagannathan (1991) bound). The empirical shape of the term structure of bond Sharpe ratios estimated in Qin, Linetsky, and Nie (2016) is generally opposite to the one described above, indicating that the martingale component in the long-term factorization is highly economically significant, complementing empirical results in Alvarez and Jermann (2005), Bakshi and Chabi-Yo (2012), Borovička, Hansen, and Scheinkman (2016), and Christensen (2016a).…”

Section: The Long-term Limitmentioning

confidence: 59%

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Long-Term Risk: A Martingale Approach

Qin¹,

Linetsky²

2017

Econometrica

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A. PROOFS FOR SECTION 3 WE FIRST RECALL SOME RESULTS about semimartingale topology originally introduced by Émery (1979) (see Czichowsky and Schweizer (2006), Kardaras (2013), andCuchiero andTeichmann (2015) for recent applications in mathematical finance). The semimartingale topology is stronger than the topology of uniform convergence in probability on compacts (ucp). In the latter case, the supremum in Eq. (2.1) is only taken over integrands in the form η t = 1 [0 s] (t) for every s > 0:The following inequality due to Burkholder is useful for proving convergence in the semimartingale topology in Theorem 3.1 (see Meyer (1972, Theorem 47, p. 50) for discrete martingales and Cuchiero and Teichmann (2015) for continuous martingales, where a proof is provided inside the proof of their Lemma 4.7).LEMMA A.1: For every martingale X and every predictable process η bounded by 1, |η t | ≤ 1, it holds that aP supfor all a ≥ 0 and t > 0.We will also use the following result (see Kardaras (2013, Proposition 2.10)).We will also make use of the following lemma.LEMMA A.3: Let (X n t ) t≥0 be a sequence of martingales such that X n t

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Section: The Long-term Limitmentioning

confidence: 59%

“…This characterization enhances our understanding of risk pricing over alternative investment horizons. The growing related literature includes Hansen (2012), Hansen andScheinkman(2012, 2017), Borovička, Hansen, and Scheinkman (2016), Bakshi and Chabi-Yo (2012), Christensen (2016aChristensen ( , 2016b, , and Qin, Linetsky, and Nie (2016).…”

Section: Introductionmentioning

confidence: 99%

Long-Term Risk: A Martingale Approach

Qin¹,

Linetsky²

2017

Econometrica

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“…This characterization enhances our understanding of risk pricing over alternative investment horizons. The growing related literature includes Hansen (2012), Hansen and Scheinkman (2012), Hansen and Scheinkman (2014), Borovička et al (2016), Bakshi and Chabi-Yo (2012), Christensen (2016a), Christensen (2016b), and .…”

Section: Introductionmentioning

confidence: 99%

Long Term Risk: A Martingale Approach

Qin¹,

Linetsky²

2014

SSRN Journal

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This paper extends the long-term factorization of the stochastic discount factor introduced and studied by in discrete-time ergodic environments and by Hansen andScheinkman (2009) andHansen (2012) in Markovian environments to general semimartingale environments. The transitory component discounts at the stochastic rate of return on the long bond and is factorized into discounting at the long-term yield and a positive semimartingale that extends the principal eigenfunction of Hansen and Scheinkman * The authors thank Lars Peter Hansen (the co-editor) and the anonymous referees for their insightful comments and suggestions that helped improve the paper, and Jaroslav Borovicka, Peter Carr, Timothy Christensen (discussant) and Jose Scheinkman for stimulating discussions. This paper is based on research supported by the grant CMMI-1536503 from the National Science Foundation.† likuanqin2012@u.northwestern.edu ‡ linetsky@iems.northwestern.edu 1 (2009) to the semimartingale setting. The permanent component is a martingale that accomplishes a change of probabilities to the long forward measure, the limit of T -forward measures. The change of probabilities from the data generating to the long forward measure absorbs the long-term risk-return trade-off and interprets the latter as the long-term risk-neutral measure.

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“…Under general conditions (see Hansen and Scheinkman (2009) and Christensen (2015Christensen ( , 2017), there exists a strictly positive function ι and scalar λ > 0 solving 9 the equation…”

Section: New Resultsmentioning

confidence: 99%

Existence and uniqueness of recursive utilities without boundedness

Christensen

2020

Preprint

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This paper derives primitive, easily verifiable sufficient conditions for existence and uniqueness of recursive utilities for a number of important classes of preferences. In order to accommodate models commonly used in practice, we allow both the statespace and per-period utilities to be unbounded. For many of the models we study, existence and uniqueness is established under a single "thin tail" condition on the distribution of growth in per-period utilities. We illustrate our approach with applications to robust preferences, models of ambiguity aversion and learning about hidden states, dynamic discrete choice models, and Epstein-Zin preferences.

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Nonparametric Identification of Positive Eigenfunctions

Cited by 17 publications

References 35 publications

Long-Term Risk: A Martingale Approach

Long-Term Risk: A Martingale Approach

Long Term Risk: A Martingale Approach

Existence and uniqueness of recursive utilities without boundedness

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