EQUILIBRIUM VALUATION OF CURRENCY OPTIONS UNDER A DISCONTINUOUS MODEL WITH CO-JUMPS

In this paper, we study the equilibrium valuation for currency options in a setting of the two-country Lucas-type economy. Different from the continuous model in Bakshi and Chen [1], we propose a discontinuous model with jump processes. Empirical findings reveal that the jump components in each country's money supply can be decomposed into the simultaneous co-jump component and the country-specific jump component. Each of the jump components is modeled with a Poisson process whose jump intensity follows a mean reversion stochastic process. By solving a partial integro-differential equation (PIDE), we get a closed-form solution to the PIDE for a European call currency option. The numerical results show that the derived option pricing formula is efficient for practical use. Importantly, we find that the co-jump has a significant impact on option price and implied volatility.

Modeling and dynamic behavior of a discontinuous tourism-based social-ecological dynamical system

In this paper we study a four-dimensional tourism-based social-ecological system including two different types of tourists, i.e., eco-tourists and mass-tourists. First we develop the mathematical model of this system, in order to make it more realistic. In fact, the negative effects of eco-tourists on the environment can not be always ignored. Therefore, we consider a discontinuous function for describing the damage induced by tourist activities to ecosystem quality. By introducing a discontinuous model in this way, we can provide a tool for better investigating the behavior of tourism phenomenon. We analyse the dynamic of the obtained discontinuous system, by using the theory of discontinuous dynamical systems. Moreover, in order to discuss about profitability, compatibility and sustainability of the obtained system, stability regions for that will be found. Furthermore by verifying tangent points of the discontinuous system, more dynamic features of eco and mas-tourists will be shown. In this regard, we determine some regions for existence of the collision of two tangent points for the system. Some numerical simulations are carried out to demonstrate our theoretical results. Here our numerical and theoretical achievements can provide useful information for analysing the tourism industry.

The Renaissance Proto-Parametrization

The chapter proposes the definition of a workflow aimed at the BIM modeling of historical architectures referable to the classical language of Renaissance treatises. Through the experimentation on a case study conditioned by pre-existences, the authors exploit the potential offered by BIM software to contain standardized and rewritable information through the management of the temporal phases. Starting from the discontinuous model, ideal geometries are defined using a continuous mathematical language. These geometries are gradually adapted to the case study by consecutive steps of modification. The different phases of the modeling are recorded in the database, favoring the transparency of the process. HBIM thus becomes an instrument not only of modeling and documentation, but also of analysis and interpretation of the architectural complexity of the historical built heritage.

Evidentiary Earthquakes: Design and Discontinuity through Seismic Methods

The science of seismology has long wrestled with the problem of discontinuity when evaluating terrestrial phenomena such as earthquakes. Discontinuity arises between the cause of an earthquake and its resulting effects, making it difficult to ascertain what triggered such a seismic occurrence in the first place. This article revisits documented case studies of earthquakes in the United States and the impact of these tectonic upheavals using observations, quantitative measurements and narrative accounts to interrogate the so-called ordered relationship between events and their causes. Architecture as a discipline stands to gain substantial ground through the study of seismology as a discontinuous model of science and of history; diachronic frameworks for comprehending physical evidence are used to reflect on how architects may engage with geological singularities beyond analogy and formal imitation.