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

Mark Fisher

No 99-18, FRB Atlanta Working Paper from Federal Reserve Bank of Atlanta

Abstract: 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.

Keywords: Asset pricing; Consumption (Economics); Interest rates; Wealth (search for similar items in EconPapers)
Date: 1999
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Working Paper: Consumption and Asset Prices with Recursive Preferences: Continuous-Time Approximations to Discrete-Time Models (1999)
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