Intertemporal asset pricing and the marginal utility of wealth (original) (raw)

Consumption and Asset Prices with Recursive Preferences

SSRN Electronic Journal, 2000

We analyze consumption and asset pricing with recursive preferences given by Kreps-Porteus stochastic differential utility (K-P SDU). We show that utility depends on two state variables: current consumption and a second variable (related to the wealth-consumption ratio) that captures all information about future opportunities. This representation of utility reduces the internal consistency condition for K-P SDU to a restriction on the second variable in terms of the dynamics of a forcing process (consumption, the state-price deflator, or the return on the market portfolio). Solving the model for (i) optimal consumption, (ii) the optimal portfolio, and (iii) asset prices in general equilibrium amounts to finding the process for the second variable that satisfies this restriction. We show that the wealth-consumption ratio is the value of an annuity when the numeraire is changed from units of the consumption good to units of the consumption process, and we characterize certain features of the solution in a non-Markovian setting. In a Markovian setting, we provide a solution method that it quite general and can be used to produce fast, accurate numerical solutions that converge to the Taylor expansion.

Asset Pricing with Delayed Consumption Decisions

2004

The attempt to match asset price characteristics such as the risk-free interest rate, equity premium and the Sharpe ratio with data for models with instantaneous consumption decisions and time separable preferences has not been very successful. Many recent versions of asset pricing models have, in order to match those financial characteristics better with the data, employed habit formation where past consumption acts as a constraint on current consumption. In those models, surplus consumption, consumption over and above past consumption, improves welfare, yet habit formation gives rise to an additional state variable. By studying such a model we also allow for adjustment costs of investment. The asset price characteristics that one obtains from those models may depend on the solution techniques employed. In this paper a stochastic version of a dynamic programming method with adaptive grid scheme is applied to compute the above mentioned asset price characteristics where past consumption decisions are treated as an additional state variable. Since, as shown in , our method produces only negligible errors it is suitable to be used as solution technique for such models with more complicated decision structure. Using our solution methods shows that there are still remaining puzzles for the consumption based asset pricing model. JEL Classification: C60, C61, C63, D90, G12

Optimal Consumption When Income Follows a Markov Process

Bulletin of Economic Research, 1984

In econometric investigations of consumption, the econometrician may either estimate the structural relationship or investigate the implication (revealed by Hall) that the marginal utility of consumption follows a random walk. Researchers have been inhibited from following the former route by the lack of an explicit theoretical relationship. This paper removes this inhibition by deriving the optimal consumption strategy of an individual with constant absolute risk-aversion, whose income is generated by an nth order normal autoregressive process. We show that the implied structural relationship is linear in wealth and lagged income terms (up to the nth order). This facilitates informative and efficient econometric exploration of the consumption function. ' Note, however, that our model is also valid for a finite, but uncertain, lifetime if there is a constant probability (1-0) that the individual will die at the end of a givcn period given that he or she was alive a t thc beginning o f the period. In this case, all our analysis goes through if p is cvcrywhere rcplaccd by p0 (it' it is assumed that bequests yield zero utility).

Optimal consumption and investment with Lévy processes

Revista Brasileira de Economia, 2003

We study the intertemporal consumption and investment problem in a continuous time setting when the security prices follow a Geometric Lévy process. Using stochastic calculus for semimartingales we obtain conditions for the existence of optimal consumption policies. Also, we give a charaterization of the equivalent martingale measures. Estudamos o problema do consumo e investimento intertemporal em tempo contínuo, quando os preços dos ativos seguem um processo de Lévy Geométrico. Usando cálculo estócastico para semimartingalas obtemos condições para a existência de políticasótimas de consumo. Também, mostramos a caracterização das medidas martingalas equivalentes. * This paper was received in Nov. 2002 and approved in Feb. 2003. I want to thank Maria Eulália Vares for valuable comments and IMPA-Brazil, where this project was partially developed. I also acknowledge financial support from CNPq, Brazil.

Time preference and capital asset pricing models

Journal of Financial Economics, 1985

Results of the theory of individual optimal consumption-investment choice under uncertainty are extended to a class of intertemporally dependent preferences for consumption streams. These results are then used to show that with intertemporally dependent preferences, which are more realistic than the separable time-additive preference structure, Merton's (1973) multi-beta intertemporal capital asset pricing model is still valid, but it can no longer be collapsed to single consumption-beta model.