Using the Hamilton-Jacobi-Bellman equation, we derive both a Keynes-Ramsey rule and a closed form solution for an optimal consumption-investment problem with labor income. The utility function is unbounded and uncertainty stems from a Poisson process. Our results can be derived because of the...

We study a small open economy displaying Pareto-distributed wealth resulting from random death. The government runs a distribution scheme on inheritance. We present the mathematical background that allows to study the dynamics of means. We end up with ordinary differential equations for the mean...

This paper introduces the probabilistic formulation of continuous-time economic models: forward stochastic differential equations (SDE) govern the dynamics of backward-looking variables, and backward SDEs capture that of forward-looking variables. Deep learning streamlines the search for the...

In this paper we focus on specification of revenue functions in their dual price space. We consider two distance functions, both dual to the revenue function: Shephard output distance function and the directional output distance function, both in price space. The former is multiplicative,...

This paper revisits the debate about the appropriate differential equation that governs the evolution of knowledge in models of endogenous growth. We argue that the assessment of the appropriateness of an equation of motion should not only be based on its implications for the future, but that it...

The focus is upon equilibrium real exchange rates, optimal external debt and their interaction, in a world where both the return on investment and the real rate of interest are stochastic variables. These theoretically based measures are applied empirically to answer the following questions:...

We analyze optimal harvesting policy under stochastic price and stock dynamics. We state a set of weak conditions under which the optimal policy can be characterized by a single exercise threshold and show that the value of optimal harvesting and depletion policies can be expressed as the...

Standard explanations for the income heterogeneity within neighborhoods rely on differences of preferences across households and heterogeneity of the housing stock. We propose an alternative and complementary explanation. We construct a stochastic equilibrium sorting model where (1) income is...