Recursive Utility and Thompson Aggregators I: Constructive Existence Theory for the Koopmans Equation

Koopmans recursive preferences and income convergence

Stiglitz (Econometrica 37 (1969) 382) shows income convergence in a many-agent Solow growth model with integrated capital markets (ICM). The many-agent Ramsey model (MARM) without ICM also gives income convergence. With a MARM, equal discount rates, and ICM, convergence of incomes (as opposed to product per capita) cannot occur. These results depend upon fixed saving propensities (Stiglitz) or ...

A Constructive Proof of the Existence of a Utility in Revealed Preference Theory

Within the context of the standard model of rationality within economic modelling we show the existence of a utility function that rationalises a demand correspondence, hence completely characterizes the associated preference structure, by taking a dense demand sample. This resolves the problem of revealed preferences under some very mild assumptions on the demand correspondence which are close...

Recursive Utility : Discrete Time Theory ∗

Optimal Existence and Uniqueness Theory for the Fractional Heat Equation

We construct a theory of existence, uniqueness and regularity of solutions for the fractional heat equation ∂tu + (−∆) s u = 0, 0 < s < 1, posed in the whole space R with data in a class of locally bounded Radon measures that are allowed to grow at infinity with an optimal growth rate. We consider a class of nonnegative weak solutions and prove that there is an equivalence between nonnegative d...

Constructive Induction for Recursive Programs

This paper presents an algorithm for inducing recursive rst order Horn clause programs from examples without background knowledge. This algorithm invents new predicates and their de nitions exhaustively until the instances of a new predicate become the same as examples except for the name of the predicate. Our system CIRP switches into constructive induction mode using a new heuristic taking ad...