Stability of equilibrium asset pricing models: A necessary and sufficient condition

Jaroslav Borovička; John Stachurski

doi:10.1016/j.jet.2021.105227

Stability of equilibrium asset pricing models: A necessary and sufficient condition

Jaroslav Borovička, John Stachurski

Research output: Contribution to journal › Article › peer-review

Abstract

We obtain an exact necessary and sufficient condition for the existence and uniqueness of equilibrium asset prices in infinite horizon, discrete-time, arbitrage free environments. Using local spectral radius methods, we connect the condition, and hence the problem of existence and uniqueness of asset prices, with the recent literature on stochastic discount factor decompositions. Our results include a globally convergent method for computing prices whenever they exist. Convergence of this iterative method itself implies both existence and uniqueness of equilibrium asset prices.

Original language	English (US)
Article number	105227
Journal	Journal of Economic Theory
Volume	193
DOIs	https://doi.org/10.1016/j.jet.2021.105227
State	Published - Apr 2021

Keywords

Asset pricing
Equilibrium prices
Spectral methods

ASJC Scopus subject areas

Economics and Econometrics

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10.1016/j.jet.2021.105227

Cite this

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title = "Stability of equilibrium asset pricing models: A necessary and sufficient condition",

abstract = "We obtain an exact necessary and sufficient condition for the existence and uniqueness of equilibrium asset prices in infinite horizon, discrete-time, arbitrage free environments. Using local spectral radius methods, we connect the condition, and hence the problem of existence and uniqueness of asset prices, with the recent literature on stochastic discount factor decompositions. Our results include a globally convergent method for computing prices whenever they exist. Convergence of this iterative method itself implies both existence and uniqueness of equilibrium asset prices.",

keywords = "Asset pricing, Equilibrium prices, Spectral methods",

author = "Jaroslav Borovi{\v c}ka and John Stachurski",

note = "Funding Information: We thank Ippei Fujiwara, Sean Meyn, Thomas J. Sargent, co-editor Guillermo Ordo{\~n}ez and two referees for many valuable comments and suggestions, as well as participants at the plenary lecture of the SNDE 2018 Annual symposium at Keio University. In addition, special thanks are due to Miros{\l}awa Zima for detailed discussion of local spectral radius conditions. Financial support from ARC grant FT160100423 and Alfred P. Sloan Foundation grant G-2016-7052 is also gratefully acknowledged. Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

year = "2021",

month = apr,

doi = "10.1016/j.jet.2021.105227",

language = "English (US)",

volume = "193",

journal = "Journal of Economic Theory",

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T2 - A necessary and sufficient condition

AU - Borovička, Jaroslav

AU - Stachurski, John

N1 - Funding Information: We thank Ippei Fujiwara, Sean Meyn, Thomas J. Sargent, co-editor Guillermo Ordoñez and two referees for many valuable comments and suggestions, as well as participants at the plenary lecture of the SNDE 2018 Annual symposium at Keio University. In addition, special thanks are due to Mirosława Zima for detailed discussion of local spectral radius conditions. Financial support from ARC grant FT160100423 and Alfred P. Sloan Foundation grant G-2016-7052 is also gratefully acknowledged. Publisher Copyright: © 2021 Elsevier Inc.

PY - 2021/4

Y1 - 2021/4

N2 - We obtain an exact necessary and sufficient condition for the existence and uniqueness of equilibrium asset prices in infinite horizon, discrete-time, arbitrage free environments. Using local spectral radius methods, we connect the condition, and hence the problem of existence and uniqueness of asset prices, with the recent literature on stochastic discount factor decompositions. Our results include a globally convergent method for computing prices whenever they exist. Convergence of this iterative method itself implies both existence and uniqueness of equilibrium asset prices.

AB - We obtain an exact necessary and sufficient condition for the existence and uniqueness of equilibrium asset prices in infinite horizon, discrete-time, arbitrage free environments. Using local spectral radius methods, we connect the condition, and hence the problem of existence and uniqueness of asset prices, with the recent literature on stochastic discount factor decompositions. Our results include a globally convergent method for computing prices whenever they exist. Convergence of this iterative method itself implies both existence and uniqueness of equilibrium asset prices.

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KW - Equilibrium prices

KW - Spectral methods

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JF - Journal of Economic Theory

SN - 0022-0531

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ER -

Stability of equilibrium asset pricing models: A necessary and sufficient condition

Abstract

Keywords

ASJC Scopus subject areas

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