The entity problem ABSTRACT

The entity problem
Rodríguez-Puerta, Inmaculada
Departamento de Economía, Métodos Cuantitativos e Historia Económica
Universidad Pablo de Olavide
Álvarez López, Alberto A.
Departamento de Teoría Económica y Economía Matemática
UNED
ABSTRACT
This paper presents a new model that we have referred to as the entity problem. This model
consists, on the one hand, of an entity (company or government) that wishes to obtain a specific
amount of funding and, to that end, issues risk-free assets. On the other hand, it consists of a
group of investors with the characteristics of the standard portfolio model. Under these
conditions, the goal of each investor is to maximize the expected utility of the profit, while the
goal of the entity is to obtain the desired amount of funding by minimizing the risk-free rate
offered to the investors. To solve this problem, we develop an algorithm that not only provides
this minimal rate, but also determines which investors allow the entity to achieve its goal and
establishes a preference ranking among them. This preference order is determined by what we
haven amedthres hold rate of each investor. We then study the impact of the utility function and
other parameters of the model on that preference order. In addition, we analyse two different
variants of the problem by considering homogeneity among the investors, and then assuming
the existence of a minimal rate for the risk-free asset. All the models are illustrated numerically
and on especific case is studied.