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Continuous time one-dimensional asset-pricing models with analytic price–dividend functions

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Abstract

A continuous time one-dimensional asset-pricing model can be described by a second-order linear ordinary differential equation which represents equilibrium or a no-arbitrage condition within the economy. If the stochastic discount factor and dividend process are analytic, then the resulting differential equation has analytic coefficients. Under these circumstances, the one-dimensional Cauchy–Kovalevsky Theorem can be used to prove that the solution to such an asset-pricing model is analytic. Also, this theorem allows for the development of a recursive rule, which speeds up the computation of an approximate solution. In addition, this theorem yields a uniform bound on the error in the numerical solution. Thus, the Cauchy–Kovalevsky Theorem yields a quick and accurate solution of many known asset-pricing models.

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Authors and Affiliations

  1. Department of Mathematics, Idaho State University, Pocatello, ID, 83209, USA

    Yu Chen

  2. Department of Finance, Mendoza College of Business, University of Notre Dame, Notre Dame, USA

    Thomas F. Cosimano

  3. Department of Mathematics, University of Notre Dame, Notre Dame, USA

    Alex A. Himonas

Authors
  1. Yu Chen
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  2. Thomas F. Cosimano
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  3. Alex A. Himonas
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Correspondence to Thomas F. Cosimano.

Additional information

We would like to thank seminar participants at Erasmus University, Georgia State University, the University of Notre Dame, Texas A&M University, The 2007 Summer Econometric Society Meeting at Duke University, The 12th International Conference for Computing in Economics and Finance at HEC Montreal, and The 2007 Institute for Computational Economics Workshop at University of Chicago for helpful comments. Discussions with Michael Brennan, Ralph Chami, George Constantinides, Darrell Duffie, Michael Gapen, Jennifer Gorsky, Thomas Gresik, Lars Hansen, James Holmes, Kenneth Judd, Adam Speight, and Jessica Whacter helped in the preparation of this work. We also benefited from the careful reading of the manuscript by the participants, David Karapetyan, Peter Kelly, Kate Manley, Jonathan Poelhuis, Jimmy Zhu, in the summer workshop on mathematical methods in financial economics at Notre Dame. We also benefited from the advice of the editor Charalambos Aliprantis. Tom Cosimano received financial support from the Center for Research in Financial Services Industry at The University of Notre Dame.

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Chen, Y., Cosimano, T.F. & Himonas, A.A. Continuous time one-dimensional asset-pricing models with analytic price–dividend functions. Econ Theory 42, 461–503 (2010). https://doi.org/10.1007/s00199-008-0404-2

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  • DOI: https://doi.org/10.1007/s00199-008-0404-2

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