Consumption and asset prices with recursive preferences: Continuous-time approximations to discrete-time models

Arbeitspapier

This paper presents tractable and efficient numerical solutions to general equilibrium models of asset prices and consumption where the representative agent has recursive preferences. It provides a discrete-time presentation of the approach of Fisher and Gilles (1999), treating continuous-time representations as approximations to discrete-time "truth." First, exact discrete-time solutions are derived, illustrating the following ideas: (i) The price-dividend ratio (such as the wealth-consumption ratio) is a perpetuity (the canonical infinitely lived asset), the value of which is the sum of dividend-denominated bond prices, and (ii) the positivity of the dividend-denominated asymptotic forward rate is necessary and sufficient for the convergence of value function iteration for an important class of models. Next, continuous-time approximations are introduced. By assuming the size of the time step is small, first-order approximations in the step size provide the same analytical flexibility to discrete-time modeling as Ito's lemma provides in continuous time. Moreover, it is shown that differential equations provide an efficient platform for value function iteration. Last, continuous-time normalizations are adopted, providing an efficient solution method for recursive preferences.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: Working Paper ; No. 99-18

Klassifikation und Themen

• Klassifikation: Wirtschaft
• Thema: Asset pricing ; Consumption (Economics) ; Interest rates ; Wealth

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Fisher, Mark
• Ereignis: Veröffentlichung
• (wer): Federal Reserve Bank of Atlanta
• (wo): Atlanta, GA
• (wann): 1999

Weitere Informationen

• Handle: http://hdl.handle.net/10419/100879
• Letzte Aktualisierung: 10.03.2025, 11:42 MEZ