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1
artículo
Numeric methods are effective tools to solve science or engineering problems , which use deterministic differential equations. We have Euler’s and Heun’s methods and Runge- Kutta’s schemes. Unfortunately, these algorithms don’t work with stochastic differential equations. The main application is referred to the utilization of stochastic calculus in the financial area. The Black-Scholes and Merton model of the price values option in the financial markets is expressed by the Brownian movement and the stochastic differential equation, proposing the financial derivatives valorization by means of the stochastic calculus.
2
artículo
Numeric methods are effective tools to solve science or engineering problems , which use deterministic differential equations. We have Euler’s and Heun’s methods and Runge- Kutta’s schemes. Unfortunately, these algorithms don’t work with stochastic differential equations. The main application is referred to the utilization of stochastic calculus in the financial area. The Black-Scholes and Merton model of the price values option in the financial markets is expressed by the Brownian movement and the stochastic differential equation, proposing the financial derivatives valorization by means of the stochastic calculus.
3
artículo
Using the ordinary differential equation of motion it is possible to determine the position in time of a mass that moves because it is disturbed by some deterministic action. For this work it was proposed to model a mass supporting a random disturbance. To do this, it was required to model Brownian motion since it efficiently represents the randomness of the phenomenon. Using the fundamentals of Functional Analysis, Probability Theory and Stochastic Processes, a stochastic differential equation of motion was obtained. In order to extract solutions from this equation, the Euler-Maruyama method was used, which was implemented computationally. The results obtained showed that the use of a non-deterministic version to model movement generates satisfactory results and of interest to science.
4
tesis de grado
Las reacciones químicas autocatalíticas dan lugar a fenómenos complejos como las reacciones oscilatorias y la formación de patrones químicos. Experimentos en las reacciones de Belousov-Zhabotinsky y de iodato-ácido arsenioso (entre otras) exhiben frentes de reacción que separan reactivos de productos de la reacción. La propagación de los frentes es debida al efecto conjunto de la reacción y la difusión molecular. La mayoría de los estudios teóricos en estos sistemas se basan en modelos deterministas. Sin embargo, al realizar experimentos, fluctuaciones aleatorias estarán presentes. El objetivo de este trabajo es realizar un análisis numérico de los efectos del ruido externo en frentes de reacción-difusión. Nos enfocamos en un sistema c ́ubico de reacción-difusión con dos especies químicas que poseen distintos coeficientes de difusión. Al propagarse en dominios bidi...
5
artículo
Purpose. The purpose of this article is to propose a detailed methodology to estimate, model and incorporate the non-constant volatility onto a numerical tree scheme, to evaluate a real option, using a quadrinomial multiplicative recombination. Design/methodology/approach. This article uses the multiplicative quadrinomial tree numerical method with non-constant volatility, based on stochastic differential equations of the GARCH-diffusion type to value real options when the volatility is stochastic. Findings. Findings showed that in the proposed method with volatility tends to zero, the multiplicative binomial traditional method is a particular case, and results are comparable between these methodologies, as well as to the exact solution offered by the Black–Scholes model. Originality/value. The originality of this paper lies in try to model the implicit (conditional) market volatility ...
6
artículo
The present article has as a goal to show an alternative way for deriving the Black-Scholes equation using the Schrödinger equation of quantum mechanics, taking into account that both of these partial differential equations are quite similar.
7
artículo
Publicado 2022
Enlace
Enlace
In this communication, a fractional order design and numerical form of the solutions are presented for numerical simulations of heterogeneous mosquito model. The use of the fractional order derivatives is exploited to observe more accurate and exhaustive performances of the numerical simulation of the model. The novel design of the fractional order heterogeneous mosquito differential system is analyzed with stochastic solver based on the internet of things (IoT) technologies, represented with four categories i.e., normal individuals, people with reflex behavior, panic behavior and controlled behavior based differential system. The solutions of the novel design of the fractional order system are presented by using the stochastic paradigm of artificial neural network (ANN) procedures along with the Scaled Conjugate Gradient (SCG), i.e., ANN-SCG, for learning of weights. In ANN-SCG implemen...
8
artículo
Publicado 2022
Enlace
Enlace
Classifying small agricultural producers based on their technical efficiency and economic performance allows us to gauge the potential to improve yield in the quinoa crop, promote local food security, and improve rural incomes. Consequently, the objective of this study was to characterize and classify quinoa producers at the Peruvian Altiplano based on their productive, economic, and social attributes, so the technical efficiency and economic performance of the identified groups can be analyzed. Hence, 409 surveys conducted among quinoa producers in the Puno region were used to run the statistical analysis using two-stage cluster techniques, stochastic frontier, linear regression, and ANOVA tests. The results revealed that three groups of producers exhibited discriminating variables in the use of fertilizers, organic fertilizers, weed control, application of fungicides, production of qui...
9
artículo
Purpose: The Spanish airport system contains several regional airports within an amenity distance and alternative travel modes. Profitable airports cross-subsidise small airports, which are not required for regional development or connectivity. Airports are government-owned and centralised-managed by Spanish Airports and Air Navigation (AENA, for its Spanish acronym). This study aims to analyse the probability of an under-used public infrastructure and the AENA’s managerial ability as per the financial sustainability of the network in the long term. Design/methodology/approach: The national regulatory framework determines the airports’ environment. Six airports revealed unobserved heterogeneity, avoiding model misspecification. The framework is defined through proxies of the singularities of the Spanish framework: public investments and geographical specifications. The stochastic fro...
10
tesis de grado
Publicado 2020
Enlace
Enlace
The Incoherent Scatter Radar (ISR) technique provides an important tool for ionospheric plasma parameter estimation through the calculation of the electron density spectrum. This quantity is constrained to the ionospheric approximations considered. If these are very realistic, finding an analytical expression for the terms involve in the electron density spectrum could be impossible. In that sense, using the mathematical tool known as stochastic differential equation (SDE) is required. Because of the nature of the equation described the ionospheric particle dynamics, called Langevin equation, stochastic numerical methods have to be studied. In this work, we will present a review of ISR theory and the connection to SDE. Moreover, we list three different methods, which are used to analyze the collisional and magnetized approximation of the ionosphere.
11
tesis de maestría
Publicado 2023
Enlace
Enlace
Los incendios forestales se han venido incrementando en las últimas cuatro décadas a nivel mundial. En el Perú de acuerdo a los datos del INDECI, en los últimos 10 años se evidencia una tendencia creciente. La ocurrencia de estos eventos representa la degradación de la calidad del aire, de la flora y pone en grave riesgo a muchas personas y zonas agrícolas. Para una adecuada evaluación de uno de los componentes del riesgo generado por estos eventos, se requiere analizar la intensidad de su ocurrencia a través de herramientas flexibles. En este contexto se estudia el patrón puntual de estos eventos, a través del modelo espacial bayesiano de Cox log-gaussiano (LGCP) bajo el enfoque de ecuaciones diferenciales parciales estocásticas (SPDE). Los distintos modelos que se evalúan corresponden a la clase de modelos gaussianos latentes y jerárquicos, lo cual nos permite realizar su...
12
artículo
The radiation pathway through a medium where occur the absorption, scattering and emission phenoma is described by the radiative transfer equation (ETR). For purely absorbing media, the dispersion phenomenon is neglected by reducing the ETR to a linear differential equation with analytical solution. For dispersive media, the ETR is a nonlinear differential equation, with non analytical solution and the solution must be approximated by deterministic numerical methods. Monte Carlo is a stochastic method based in probabilities and use random numbers to simulate the occurrence of an event, in this case, the pathways radiation in a participating media. In this study, we have used finite difference and discrete ordinates methods to solve the ETR in one dimension, the results were compared with the Monte Carlo results, Test case results are presented, also the source code used for the solution ...
13
tesis de grado
Publicado 2020
Enlace
Enlace
The Incoherent Scatter Radar (ISR) technique provides an important tool for ionospheric plasma parameter estimation through the calculation of the electron density spectrum. This quantity is constrained to the ionospheric approximations considered. If these are very realistic, finding an analytical expression for the terms involve in the electron density spectrum could be impossible. In that sense, using the mathematical tool known as stochastic differential equation (SDE) is required. Because of the nature of the equation described the ionospheric particle dynamics, called Langevin equation, stochastic numerical methods have to be studied. In this work, we will present a review of ISR theory and the connection to SDE. Moreover, we list three different methods, which are used to analyze the collisional and magnetized approximation of the ionosphere.
14
artículo
Publicado 2022
Enlace
Enlace
The current work aims to design a computational framework based on artificial neural networks (ANNs) and the optimization procedures of global and local search approach to solve the nonlinear dynamics of the spread of COVID-19, i.e., the SEIR-NDC model. The combination of the Genetic algorithm (GA) and active-set approach (ASA), i.e., GA-ASA, works as a global-local search scheme to solve the SEIR-NDC model. An error-based fitness function is optimized through the hybrid combination of the GA-ASA by using the differential SEIR-NDC model and its initial conditions. The numerical performances of the SEIR-NDC nonlinear model are presented through the procedures of ANNs along with GA-ASA by taking ten neurons. The orrectness of the designed scheme is observed by comparing the obtained results based on the SEIR-NDC model and the reference Adams method. The absolute error performances are perf...
15
tesis de maestría
Publicado 2023
Enlace
Enlace
Los incendios forestales se han venido incrementando en las últimas cuatro décadas a nivel mundial. En el Perú de acuerdo a los datos del INDECI, en los últimos 10 años se evidencia una tendencia creciente. La ocurrencia de estos eventos representa la degradación de la calidad del aire, de la flora y pone en grave riesgo a muchas personas y zonas agrícolas. Para una adecuada evaluación de uno de los componentes del riesgo generado por estos eventos, se requiere analizar la intensidad de su ocurrencia a través de herramientas flexibles. En este contexto se estudia el patrón puntual de estos eventos, a través del modelo espacial bayesiano de Cox log-gaussiano (LGCP) bajo el enfoque de ecuaciones diferenciales parciales estocásticas (SPDE). Los distintos modelos que se evalúan corresponden a la clase de modelos gaussianos latentes y jerárquicos, lo cual nos permite realizar su...
16
tesis de grado
Publicado 2020
Enlace
Enlace
Universidad Nacional Agraria La Molina. Facultad de Economía y Planificación. Departamento Académico de Economía y Planificación
