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.
Intertemporal asset pricing and the marginal utility of wealth
Battauz, Anna;De Donno, Marzia;Ortu, Fulvio
2011
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.File | Dimensione | Formato | |
---|---|---|---|
IAPMU.pdf
non disponibili
Tipologia:
Documento in Pre-print (Pre-print document)
Licenza:
NON PUBBLICO - Accesso privato/ristretto
Dimensione
331.97 kB
Formato
Adobe PDF
|
331.97 kB | Adobe PDF | Visualizza/Apri |
1-s2.0-S0304406811000371-main.pdf
non disponibili
Descrizione: Articolo
Tipologia:
Pdf editoriale (Publisher's layout)
Licenza:
NON PUBBLICO - Accesso privato/ristretto
Dimensione
593.95 kB
Formato
Adobe PDF
|
593.95 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.