Exploration of Entropy on Decision Models. Nonlinear Dependence, Utility and Socio-Economics Welfare Analysis

Traditionally the approaches used in economy and finance have been based on regression models whose assumptions are essentially linear. Given the nature of the variables to be studied, this type of approach reveals some problems in the estimation level, especially because of the strong assumptions of the OLS. The increment of non stationarity and asymmetry models contributed for the assumption of nonlinearity intrinsic in this type of data.
These methodologies have been applied in more recent studies and constitute a promising field of investigation in this area. However, the types of nonlinearity captured by these models are specific and do not capture nonlinear effects of different origins not specified a priori. In order to solve this problem, we need to use general measures that capture the global nonlinearity existing in the data under study. In this context, we highlight the importance of the use of the Information Theory measures, namely entropy and mutual information.
In this way, possible developments in the extent of the focus of the present project, may consider the identification of the sources of nonlinearity in the financial time series, through the separation of the deterministic from the stochastic components, in order to provide to the investor more credible and detailed information as base for the investment decision. It is intended to study the Portuguese stock market and compare the results with some international stock markets.
Another potential application is the exploration of the entropy as uncertainty measure in decision models. Such application can be justified based on the generality of the entropy as uncertainty measure and disorder and the possibility to consider more information about the distribution of probability of the variables, than the traditionally risk and uncertainty measures used.
The utility functions of the investors that are risk averse, can be obtained using several methods, namely the maximization of entropy. This approach plays an important role in microeconomic analysis of decisions regarding contingent wealth. The study and characterization of the Portuguese investor may constitute an important contribute to this field and the development of the Portuguese research in this area.