Since the beginnings of modern economics, economists sought to emulate the revolution in physics initiated by Newton’s ‘Principia’ (1687). Concepts from mechanics have influenced economic models both in terms of methodology and content. The aim of this theoretical paper is to put forward a...

We develop a mathematical proof demonstrating that only financially-strong firms will sell put options on their own stock, but financially-weak firms will not. The sale of options on a company's own stock exposes the buyer to default risk of the issuer, which additionally complicates the payoff...

As a refinement of the concept of stationary point, the notion of perfect stationary point was formulated in the literature. Although simplicial methods could be applied to approximate such a point, these methods do not make use of the possible differentiability of the problem and can be very...

Structural estimation of macroeconomic models and new HANK-type models with extremely high dimensionality require fast and robust methods to efficiently deal with occasionally binding constraints (OBCs). This paper proposes a novel algorithm that solves for the perfect foresight path of...

We present the first necessary and sufficient conditions for the existence of a unique perfect-foresight solution, returning to a given steady-state, in an otherwise linear model with occasionally binding constraints. We derive further conditions on the existence of a solution in such models,...

Preface AuthorSymbols and Abbreviations 1. Mathematical Foundations 1 2. Mathematical Foundations 2 3. Mathematical Foundations 3 4. Mathematical Foundations 4 5. Global and Local Extrema of Real-Valued Functions 6. Global Extrema of Real-Valued Functions 7. Local Extrema of Real-Valued...

Mathematical foundations 1 -- Mathematical foundations 2 -- Mathematical foundations 3 -- Mathematical foundations 4 -- Global and local extrema of real-valued functions -- Global extrema of real-valued functions -- Local extrema of real-valued functions -- Convex and concave real-valued...