Intertemporal asset pricing and the marginal utility of wealth

52 Pages Posted: 1 Apr 2007 Last revised: 16 Feb 2012

See all articles by Anna Battauz

Anna Battauz

Bocconi University - Department of Finance

Marzia De Donno

Universita Degli Studi Di Parma

Fulvio Ortu

Bocconi University - Department of Finance

Date Written: March 30, 2007

Abstract

We consider the general class of discrete-time, …finite-horizon intertemporal asset pricing models in which preferences for consumption at the intermediate dates are allowed to be state-dependent, satiated, non-convex and discontinuous, and the information structure is not required to be generated by a Markov process of state variables. We supply a generalized de…finition of marginal utility of wealth based on the Fréchet differential of the value operator that maps time t wealth into maximum conditional remaining utility. We show that in this general case all state-price densities/stochastic discount factors are fully characterized by the marginal utility of wealth of optimizing agents even if their preferences for intermediate consumption are highly irregular. Our result requires only the strict monotonicity of preferences for terminal wealth and the existence of a portfolio with positive and bounded gross returns. We also relate our generalized notion of marginal utility of wealth to the equivalent martingale measures/risk-neutral probabilities commonly employed in derivative asset pricing theory. We supply an example in which our characterization holds while the standard representation of state-price densities in terms of marginal utilities of optimal consumption fails.

Keywords: arbitrage, viability, linear pricing rules, optimal portfolio-consumption problems, marginal utility of wealth, envelope theorem

JEL Classification: G11, G12, G13, G14, C6

Suggested Citation

Battauz, Anna and De Donno, Marzia and Ortu, Fulvio, Intertemporal asset pricing and the marginal utility of wealth (March 30, 2007). Journal of Mathematical Economics, Vol. 47, No. 2, 2011. Available at SSRN: https://ssrn.com/abstract=977467 or http://dx.doi.org/10.2139/ssrn.977467

Anna Battauz (Contact Author)

Bocconi University - Department of Finance ( email )

Via Roentgen 1
Milano, MI 20136
Italy

Marzia De Donno

Universita Degli Studi Di Parma

via Kennedy 6
Parma, 43125
Italy

Fulvio Ortu

Bocconi University - Department of Finance ( email )

Via Roentgen 1
Milano, MI 20136
Italy

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