Resumen de Modelos dinámicos (aleatorios) en la actividad empresarial. Aplicación al cálculo de un índice de pérdidas por catástrofes para la industria aseguradora
- español
En este artículo se plantea la naturaleza e importancia del análisis dinámico de la actividad empresarial. En concreto se aplica para representar la evolución de la siniestralidad derivada de la ocurrencia de sucesos de naturaleza catastrófica. El objetivo de esta modelización es calcular índices de pérdidas para la industria aseguradora. Partiendo del modelo desarrollado por Pérez-Fructuoso (2008), en el que se representa la dinámica de la variable cuantía de siniestros pendiente de declarar mediante un movimiento Browniano geométrico, en este artículo se proponen tres modelos alternativos. Seguidamente se estiman los parámetros de cada modelo propuesto y se validan los resultados obtenidos
- English
This article reviews the nature and importance of the dynamic analysis of business activity. Specifically, it describes how to represent the evolution of claims arising from the occurrence of events of a catastrophic nature. The objective of this modeling is to calculate loss rates incurred by the insurance industry through the convolution of the reported claims variable arising from each disaster. As central hypothesis of the process, we consider that the reported claims amount is obtained as the difference between the total amount of the disaster and the incurred-but-not-yet-reported claims. Based on the modeling developed by Pérez-Fructuoso (2008), in which the dynamics of this variable is represented by a geometric Brownian motion, and assuming that the claims reporting rate is constant, this article proposes three alternative models: geometric Brownian motion with an asymptotic reporting claims rate, two Brownian motions, and an Ornstein-Ulhenbeck process. Then, we estimate the parameters of each of those proposed models, and validate the results obtained from six sets of data floods in different regions of Spain, prone to suffer this kind of events. The article concludes with a discussion on the results thus obtained
