Generalized Euler Equation Errors for Discrete Time Dynamic Portfolio Choice Models

25 Pages Posted: 20 Sep 2019 Last revised: 12 Feb 2020

See all articles by Yannick Dillschneider

Yannick Dillschneider

Goethe University Frankfurt - Department of Finance

Raimond Maurer

Goethe University Frankfurt - Finance Department

Peter Schober

Goethe University Frankfurt - Department of Finance

Date Written: February 12, 2020

Abstract

The solution to dynamic portfolio choice models can be formulated in terms of a value function by the Bellman principle of optimality, which reduces the multi-period optimal policy choice problem to a sequence of one-period maximization problems. For two adjacent periods, economists compute the error of numerically obtained policies by measuring how much these policies violate the intertemporal first order conditions for the optimal policy choice problem---so-called Euler equation errors. In this paper, we derive generalized Euler equation errors for the solution to a broad class of discrete time dynamic portfolio choice models where the policies are continuous choice variables. Our key precondition is that the gradient of the value function with respect to the state variables can be approximated. This is, for example, the case when a global polynomial basis or B-spline basis functions are used for the approximation of the value function within the discrete time dynamic programming approach. We apply our theoretical results to exemplary, representative dynamic portfolio choice models.

Keywords: Dynamic portfolio choice, discrete time dynamic programming, Euler equation errors, gradient-based optimization

JEL Classification: C61, D52, D53, G11, G12

Suggested Citation

Dillschneider, Yannick and Maurer, Raimond and Schober, Peter, Generalized Euler Equation Errors for Discrete Time Dynamic Portfolio Choice Models (February 12, 2020). Available at SSRN: https://ssrn.com/abstract=3448482 or http://dx.doi.org/10.2139/ssrn.3448482

Yannick Dillschneider

Goethe University Frankfurt - Department of Finance ( email )

Theodor-W.-Adorno-Platz 3
Frankfurt, 60629
Germany

Raimond Maurer

Goethe University Frankfurt - Finance Department ( email )

Gr├╝neburgplatz 1
House of Finance
Frankfurt, 60323
Germany

Peter Schober (Contact Author)

Goethe University Frankfurt - Department of Finance ( email )

House of Finance
Theodor-W.-Adorno Platz 3
Frankfurt am Main, Hessen 60323
Germany

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