The entity problem ABSTRACT
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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.
