Envelope theorems in Banach lattices and asset pricing

Anna Battauz, Marzia De Donno, Fulvio Ortu

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We develop envelope theorems for optimization problems in which the value function takes values in a general Banach lattice. We consider both the special case of a convex choice set and a concave objective function and the more general case case of an arbitrary choice set and a general objective function. We apply our results to discuss the existence of a well-defined notion of marginal utility of wealth in optimal discrete-time, finite-horizon consumption-portfolio problems with an unrestricted information structure and preferences allowed to display habit formation and state dependency.
Lingua originaleEnglish
pagine (da-a)303-323
Numero di pagine21
RivistaMathematics and Financial Economics
Stato di pubblicazionePubblicato - 2015


  • Banach lattice
  • Envelope theorem
  • Fréchet differential.
  • Gateaux differential
  • state-dependent utility
  • value function


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