Luca Grilli

Statistical analysis of fixed income market

We present cross and time series analysis of price fluctuations in the US Treasury fixed income market. Bonds have been classified according to a suitable metric based on the correlation among them. The classification shows how the correlation among fixed income securities depends strongly on their maturity. We study also the structure of price fluctuations for single time series.

A neural networks approach to minority game

The minority game (MG) comes from the so-called “El Farol bar” problem by W.B. Arthur. The underlying idea is competition for limited resources and it can be applied to different fields such as: stock markets, alternative roads between two locations and in general problems in which the players in the “minority” win. Players in this game use a window of the global history for making their decisions, we propose a neural networks approach with learning algorithms in order to determine players strategies. We use three different algorithms to generate the sequence of minority decisions and consider the prediction power of a neural network that uses the Hebbian algorithm. The case of sequences randomly generated is also studied.

Decision Making in Financial Markets Through Multivariate Ordering Procedure

One of the main problems in managing multidimensional data for decision making is that it is impossible to define a complete ordering on multidimensional Euclidean spaces. In order to solve this problem, the scientific community has devolped more and more sofisticated tecniques belonging to the wide framework of Multivariate Statistics. Recently some authors [DR04] have proposed an ordering procedure in which the “meaningful direction” is the “worst-best”. The aim of this paper is to extend this approach considering that, especially in financial applications, variables are quantified using different scales and, as we will show, this can lead to undesired results. As a matter of fact, we show that, without an appropriate rescaling, variables with a large range of variation (rv) are “overweighted” with respect to variables with a small one.

A Duopoly with Common Renewable Resource and Incentives

In this paper, we study a duopoly model in which two symmetric firms exploit the same public renewable resource as an input for the production of a homogeneous good. We consider the case where the firms are provided with public incentives in order to prevent the resource exhaustion in a finite time horizon which coincides with the harvesting-license period. As a consequence, we consider a differential game in finite time horizon and compute the Open Loop and linear Feedback Nash Equilibria of the game. We study the social welfare and the optimal incentives polices derived from the solutions.

Quality Competition in Healthcare Services with Regional Regulators: A Differential Game Approach

This article proposes a differential game model, in order to analyze markets in which regional regulation is operative and competition is based on quality. The case we have in mind is healthcare public service, where consumers (patients) choose the provider mainly basing on the providers’ location and the quality of services, while prices play a more limited role. In most European countries, within the same State, regional (or local) providers compete on quality to attract demand. Market regulation is set at national and/or regional level. Our model highlights the features of equilibrium in such a framework and specifically investigates how the differences in product quality evolve among regions and how inter-regional demand flows behave. Differently from some available similar models, that do not take into account the regional dimension of the decision process, we find that quality differentials among regions may persist in equilibrium.

Financial time series and neural networks in a minority game context

In this paper we consider financial time series from U.S. Fixed Income Market, S&P500, DJ Eurostoxx 50, Dow Jones, Mibtel and Nikkei 225. It is well known that financial time series reveal some anomalies regarding the Efficient Market Hypothesis and some scaling behaviour, such as fat tails and clustered volatility, is evident. This suggests that financial time series can be considered as “pseudo”-random. For this kind of time series the prediction power of neural networks has been shown to be appreciable [10]. At first, we consider the financial time series from the Minority Game point of view and then we apply a neural network with learning algorithm in order to analyse its prediction power. We prove that the Fixed Income Market shows many differences from other markets in terms of predictability as a measure of market efficiency.