Consumption and Asset Prices with Recursive Preferences

摘要

We analyze consumption and asset prierential utility (K-P SDU). We show that211u001eutility depends on two state variables: current consumption and a second variable 211u001e(related to the wealth-consumption ratio) that captures all information about 211u001efuture opportunities. This representation of utility reduces the internal 211u001econsistency condition for K-P SDU to a restriction on the second variable in 211u001eterms of the dynamics of a forcing process (consumption, the state-price 211u001edeflator, or the return on the market portfolio). Solving the model for (1) 211u001eoptimal consumption, (2) the optimal portfolio, and (3) asset prices in general 211u001eequilibrium amounts to nding the process for the second variable that satises 211u001ethis restriction. We show that the wealth-consumption ratio is the value of an 211u001eannuity when the numeraire is changed from units of the consumption good to units 211u001eof the consumption process, and we characterize certain features of the solution 211u001ein a non-Markovian setting. In a Markovian setting, we provide a solution method 211u001ethat it quite general and can be used to produce fast, accurate numerical 211u001esolutions that converge to the Taylor expansion.