This paper presents the theoretical and applicative model elaborated by Harry Markowitz on the determination of the structure of the efficient securities portfolio. In this sense, in order to determine the structure of the efficient Markowitz portfolio (PE), a Lagrange function is built and...

"Problems Book to Accompany Mathematics for Economists" is intended to complement any course in quantitative methods in economics, mathematical economics for undergraduate students or introductory mathematical economics for graduate students. It is aimed as an inexpensive supplement to nearly...

In terms of regulatory and economic capital, credit risk is the most significant risk faced by banks. We implement a credit risk model - based on publicly available information . with the aim of developing a tool to monitor credit risk in a sample of large and complex banking groups (LCBGs) in...

This paper examines a Markovian model for the optimal irreversible investment problem of a firm aiming at minimizing total expected costs of production. We model market uncertainty and the cost of investment per unit of production capacity as two independent one-dimensional regular diffusions,...

We expose a weakness in an intuitive description popularly associated with the method of Lagrange multipliers and propose an alternative intuition. According to the deficient intuition, the Lagrange technique transforms a constrained optimization problem into an unconstrained optimization...

We present a mathematical analysis of the long-run behavior of genetic algorithms that are used for modeling social phenomena. The analysis relies on commonly used mathematical techniques in evolutionary game theory. Assuming a positive but infinitely small mutation rate, we derive results that...

This paper considers the production planning problem of a firm that produces a single product using a process that has multiple production lines (or machines) in parallel, each with a finite production capacity. Specifically, the firm has m parallel production lines, each with capacity of P...

A new algorithm for calibrating agent-based models is proposed, which employs a popular gradient boosting framework. Machine learning techniques are not used to develop a surrogate model, but rather assist in narrowing down the parameter space during the search for optimal parameters. Our...

We consider the problem of portfolio optimization with a correlation constraint. The frame- work is the multiperiod stochastic financial market setting with one tradable stock, stochastic income and a non-tradable index. The correlation constraint is imposed on the portfolio and the non-tradable...

Assortment optimization is an important problem in revenue management arising in industries such as online advertising, retailing and airline ticketing. We study assortment optimization under an arbitrary mixture of multi-nomial logit (MNL) models, when the universe of products is dense. In...