We develop a mathematical programming approach for the classical PSPACE - hard restless bandit problem in stochastic optimization. We introduce a hierarchy of n (where n is the number of bandits) increasingly stronger linear programming relaxations, the last of which is exact and corresponds to...

We propose a new method for solving high-dimensional dynamic programming problems and recursive competitive equilibria with a large (but finite) number of heterogeneous agents using deep learning. The „curse of dimensionality“ is avoided due to four complementary techniques: (1) exploiting...

Krylov subspace methods have proven to be powerful methods for solving sparse linear systems arising in several engineering problems. More recently, these methods have been successfully applied in computational economics, for instance in the solution of forward-looking macroeconometric models...

We propose a new method for solving high-dimensional dynamic programming problems and recursive competitive equilibria with a large (but finite) number of heterogeneous agents using deep learning. The "curse of dimensionality" is avoided due to four complementary techniques: (1) exploiting...

Facing an hypothetical, but increasingly, case of default risk on a mortgage or a fall in interest rates, an important issue raised by the borrower is the possibility of minimizing that risk by selecting the best refinancing option. In this paper, a mortgage refinancing model is presented,...

We study general dynamic programming problems with continuous and discrete choices and general constraints. The value functions may have kinks arising (1) at indifference points between discrete choices and (2) at constraint boundaries. Nevertheless, we establish a general envelope theorem:...

The computational time required to solve and estimate dynamic economic models is one of the main constraints in empirical research. The Endogenous Grid Method (EGM) proposed by Carroll (2006) is known to offer impressive speed gains over more traditional stochastic dynamic programming methods,...

A review of the basic theory of optimal open-source software contributions points to three key factors affecting supply: non-pecuniary benefits, future expected monetary returns, and open-source licence type. This paper argues that existing large-scale software developer surveys are inadequate...

This paper relates recursive utility in continuous time to its discrete-time origins and provides a rigorous and intuitive alternative to a heuristic approach presented in [Duffie, Epstein 1992], who formally define recursive utility in continuous time via backward stochastic differential...

The paper studies a repeated contest when contestants are uncertain about their true abilities. A favourable belief about one’s own ability (confidence) stimulates effort and increases the likelihood of success. Success, in turn, reinforces favourable beliefs. We consider a specific example in...