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...

Theoretical and experimental studies of noncooperative games increasingly recognize Nash equilibrium as a limiting outcome of players repeated interaction. This note, while sharing that view, illustrates and advocates combined use of convex optimization and differential equations, the purpose...

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...

This paper analyses the direct and indirect trade volume and trade cost effects of uncertainty on international trade and economic welfare using a structural gravity framework for a panel of 97 developed and developing countries from 2000 to 2018. Our results suggest that an increase in...

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...

Generative Artificial Intelligence (AI) holds the potential to either complement knowledge workers by increasing their productivity or substitute them entirely. We examine the short-term effects of the recent release of the large language model (LLM), ChatGPT, on the employment outcomes of...

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...