Davide Radi

A prey-predator fishery model with endogenous switching of harvesting strategy

We propose a dynamic model to describe a fishery where both preys and predators are harvested by a population of fishermen who are allowed to catch only one of the two species at a time. According to the strategy currently employed by each agent, i.e. the harvested variety, at each time period the population of fishermen is partitioned into two groups, and an evolutionary mechanism regulates how agents dynamically switch from one strategy to the other in order to improve their profits. Among the various dynamic models proposed, the most realistic is a hybrid system formed by two ordinary differential equations, describing the dynamics of the interacting species under fishing pressure, and an impulsive variable that evolves in a discrete time scale, in order to describe the changes of the fraction of fishermen that harvest a given stock. The aim of the paper is to analyze the economic consequences of this kind of self-regulating fishery, as well as its biological sustainability, in comparison with other regulatory policies. Our analytic and numerical results give evidence that in some cases this kind of myopic, evolutionary self-regulation might ensure a satisfactory trade-off between profit maximization and resource conservation.

The role of constraints in a segregation model: The symmetric case

In this paper we study the effects of constraints on the dynamics of an adaptive segregation model introduced by Bischi and Merlone (2011) [3]. The model is described by a two dimensional piecewise smooth dynamical system in discrete time. It models the dynamics of entry and exit of two populations into a system, whose members have a limited tolerance about the presence of individuals of the other group. The constraints are given by the upper limits for the number of individuals of a population that are allowed to enter the system. They represent possible exogenous controls imposed by an authority in order to regulate the system. Using analytical, geometric and numerical methods, we investigate the border collision bifurcations generated by these constraints assuming that the two groups have similar characteristics and have the same level of tolerance toward the members of the other group. We also discuss the policy implications of the constraints to avoid segregation.

On a discrete-time model with replicator dynamics in renewable resource exploitation

We consider a discrete-time version of the model proposed by Lamantia and Radi [15] to describe a fishery where a population regulated by a logistic growth function is exploited by a pool of agents that can choose, at each time period, between two different harvesting strategies according to a profit-driven evolutionary selection rule. The resulting discrete dynamical system, represented by a two-dimensional nonlinear map, is characterized by the presence of invariant lines on which the dynamics are governed by one-dimensional restrictions that represent pure, i.e. adopted by all players, strategies. However, interesting dynamics related to interior attractors, where players playing both strategies coexist, are evidenced by analytical as well as numerical methods that reveal local and global bifurcations.

Opinion Dynamics on Networks

Sociophysics has devoted a lot of attention to social influence and opinion dynamics. Among the others, the pioneering works by Galam, where agents randomly gather in groups of different size until consensus is reached, have been used to analyze the spreading of rumors. Galam’s model however, considers only special kinds of social spaces. In this chapter we survey some of the most recent contributions on opinion dynamics, illustrate Galam’s model of rumor diffusion and extend it to consider more general networks.

Dynamic Modeling in Renewable Resource Exploitation

This chapter reviews some fundamental models related to the exploitation of a renewable resource, an important topic when dealing with regional economics. The chapter starts by considering the growth models of an unexploited population and then introduces commercial harvesting. Still maintaining a dynamic perspective, an analysis of equilibrium situations is proposed for a natural resource under various market structures (monopoly, oligopoly and open access). The essential dynamic properties of these models are explained, as well as their main economic insights. Moreover, some key assumptions and tools of intertemporal optimal harvesting are recalled, thus providing an interesting application of the theory of optimal growth.

A NOTE ON FERGUSSON AND PLATEN: “APPLICATION OF MAXIMUM LIKELIHOOD ESTIMATION TO STOCHASTIC SHORT RATE MODELS”

In a very recent and interesting paper, Fergusson and Platen (2015) investigate the applicability of the maximum likelihood (ML) method for estimating the parameters of some of the most popular stochastic models for the short interest rate. One of the main results of this paper is the analytical expression of the so-called observed Fisher information matrix for the Vasicek model at the ML point. However, in such a matrix some entries are not derived correctly and one entry is left unspecified. In the following, we provide the correct analytical expression of that matrix.

Minority influence in opinion spreading

Social influence has been an object of interest of social psychology for a long time. More recently, sociophysics and Galams model provide an explanation of rumors spreading in a population explaining some interesting social phenomena as diffusion of false information. Although Galams model and its recent formalizations are suitable to describe some social behavior, they take into account populations with homogeneous agents. Some recent contributions consider agents who do not change opinion and in some cases are able to persuade the others. Starting from social psychology studies about the role of specific seat occupation we provide a heterogeneous model in which those holding minority opinions can strategically choose specific social gatherings to exert their influence. We simulate the opinion dynamics comparing situations in which there is the minority to others with homogeneous agents. Our results show how the opinion dynamics is affected by the presence of such a minority.

Knowledge Spillovers, Congestion Effects, and Long-Run Location Patterns

We introduce an evolutionary two-country model to characterize long run location patterns of the manufacturing activities of competing multinational enterprises. Firms located in country 1 can decide to offshore their manufacturing activities to country 2. The profitability of production in a country depends on several factors: unitary costs of production, the number of firms that are located in each country, within-country spillovers, and cross-border spillovers. Furthermore, profits in country 2 are influenced by congestion costs. Country 1 is assumed to be technologically advanced and has an advantage in terms of internal spillovers. In contrast, country 2 offers lower production unit cost which, however, may be offset by congestion costs. The firms’ (re)location choices are based on a simple comparison of current production costs obtained in the two countries and the dynamics of switching is modeled by a simple replicator dynamics. The global analysis of the resulting one-dimensional dynamical system reveals that a large advantage in terms of unitary production costs encourages the firms to off-shore manufacturing activities to country 2. This off-shoring process stops when congestion costs offset this advantage of country 2, even though congestion costs do not cause all manufacturing activities to be re-shored to country 1. The re-shoring process can be accelerated by an increase of within-country spillovers in country 1, while cross-border spillovers tend to favor a geographic dispersion of manufacturing activities and make location patterns that lead to suboptimal long run outcomes less likely.

Computing the survival probability in the Madan–Unal credit risk model: application to the CDS market

We obtain a quasi-analytical approximation of the survival probability in the credit risk model proposed in [Madan, D.B. and Unal, H., Pricing the risk of default. Rev. Deriv. Res., 1998, 2(2), 121–160]. Such a formula, which extensive numerical simulations reveal to be accurate and computationally fast, can also be employed for pricing credit default swaps (CDSs). Specifically, we derive a quasi-analytical approximate expression for CDS par spreads, and we use it to estimate the parameters of the model. The results obtained show a rather satisfactory agreement between theoretical and real market data.

Valuing investment projects under interest rate risk: empirical evidence from European firms

ABSTRACT In this article, we perform an empirical investigation of the effect of the interest rate uncertainty on the valuation of investment projects. The analysis is carried out by employing a real option approach and by considering a set of firms that operate in various production sectors in the euro area. In particular, the revenues generated by the investment projects are modelled using a geometric Brownian motion, whereas the interest rate is specified as a stochastic process of Vasicek type. Moreover, using the volatility of the equity return as a proxy, the volatility of the revenues is calibrated to real firm data, while the parameters of the interest rate model are estimated by fitting the Euribor time series. To this aim, an ad hoc calibration procedure is developed which is based on the maximum likelihood principle and thus has the merit of being simple, fast and suitable for practical purposes. Our study reveals that the interest rate uncertainty reduces the valuation of investment projects. However, stochastic interest rates do not provide a substantial improvement with respect to constant interest rates, or at least the differences are not statistically significant.