scholarly journals On the Consistency of a Firm’s Value with a Lognormal Diffusion Process

2012 ◽  
Vol 02 (01) ◽  
pp. 31-37
Author(s):  
Andrew M. K. Cheung ◽  
Van Son Lai
Keyword(s):  
Diffusion Process ◽  
Lognormal Diffusion Process

scholarly journals Stochastic Diffusion Process Based on Generalized Brody Curve: Application to Real Data

2021 ◽  
Vol 2 (1) ◽  
pp. 01-11
Author(s):  
Ahmed Nafidi ◽  
Oussama Rida ◽  
Boujemaa Achchab
Keyword(s):  
Diffusion Process ◽  
Transition Density ◽  
Real Data ◽  
Parameters Estimation ◽  
Likelihood Method ◽  
Stochastic Diffusion ◽  
Life Expectancy At Birth ◽  
Transition Density Function ◽  
Lognormal Diffusion Process ◽  
Trend Functions

A new stochastic diffusion process based on Generalized Brody curve is proposed. Such a process can be considered as an extension of the nonhomogeneous lognormal diffusion process. From the corresponding Itô’s stochastic differential equation (SDE), firstly we establish the probabilistic characteristics of the studied process, such as the solution to the SDE, the probability transition density function and their distribution, the moments function, in particular the conditional and non-conditional trend functions. Secondly, we treat the parameters estimation problem by using the maximum likelihood method in basis of the discrete sampling, thus we obtain nonlinear equations that can be solved by metaheuristic optimization algorithms such as simulated annealing and variable search neighborhood. Finally, we perform a simulation studies and we apply the model to the data of life expectancy at birth in Morocco.

FORECASTING FOR THE UNIVARIATE LOGNORMAL DIFFUSION PROCESS WITH EXOGENOUS FACTORS

2003 ◽  
Vol 34 (8) ◽  
pp. 709-724 ◽  
Author(s):  
R. GUTIÉRREZ ◽  
P. ROMÁN ◽  
D. ROMERO ◽  
F. TORRES
Keyword(s):  
Diffusion Process ◽  
Exogenous Factors ◽  
Lognormal Diffusion Process

scholarly journals Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1062 ◽  
Author(s):  
Ahmed Nafidi ◽  
Ghizlane Moutabir ◽  
Ramón Gutiérrez-Sánchez
Keyword(s):  
Diffusion Process ◽  
Real Data ◽  
Convertible Bond ◽  
Financial Mathematics ◽  
Continuous Sampling ◽  
Statistical Computation ◽  
Likelihood Approach ◽  
Lognormal Diffusion Process ◽  
Trend Functions ◽  
The One

In this paper, we study the one-dimensional homogeneous stochastic Brennan–Schwartz diffusion process. This model is a generalization of the homogeneous lognormal diffusion process. What is more, it is used in various contexts of financial mathematics, for example in deriving a numerical model for convertible bond prices. In this work, we obtain the probabilistic characteristics of the process such as the analytical expression, the trend functions (conditional and non-conditional), and the stationary distribution of the model. We also establish a methodology for the estimation of the parameters in the process: First, we estimate the drift parameters by the maximum likelihood approach, with continuous sampling. Then, we estimate the diffusion coefficient by a numerical approximation. Finally, to evaluate the capability of this process for modeling real data, we applied the stochastic Brennan–Schwartz diffusion process to study the evolution of electricity net consumption in Morocco.

APPROXIMATING THE NONHOMOGENEOUS LOGNORMAL DIFFUSION PROCESS VIA POLYNOMIAL EXOGENOUS FACTORS

2006 ◽  
Vol 37 (4) ◽  
pp. 293-309 ◽  
Author(s):  
R. Gutiérrez ◽  
N. Rico ◽  
P. Román ◽  
D. Romero ◽  
J. J. Serrano ◽  
...  
Keyword(s):  
Diffusion Process ◽  
Exogenous Factors ◽  
Lognormal Diffusion Process

scholarly journals T-Growth Stochastic Model: Simulation and Inference via Metaheuristic Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 959
Author(s):  
Antonio Barrera ◽  
Patricia Román-Román ◽  
Francisco Torres-Ruiz
Keyword(s):  
Stochastic Model ◽  
Diffusion Process ◽  
Model Simulation ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Procedure ◽  
Metaheuristic Algorithms ◽  
Mathematical Treatment ◽  
Linear Differential ◽  
Lognormal Diffusion Process

The main objective of this work is to introduce a stochastic model associated with the one described by the T-growth curve, which is in turn a modification of the logistic curve. By conveniently reformulating the T curve, it may be obtained as a solution to a linear differential equation. This greatly simplifies the mathematical treatment of the model and allows a diffusion process to be defined, which is derived from the non-homogeneous lognormal diffusion process, whose mean function is a T curve. This allows the phenomenon under study to be viewed in a dynamic way. In these pages, the distribution of the process is obtained, as are its main characteristics. The maximum likelihood estimation procedure is carried out by optimization via metaheuristic algorithms. Thanks to an exhaustive study of the curve, a strategy is obtained to bound the parametric space, which is a requirement for the application of various swarm-based metaheuristic algorithms. A simulation study is presented to show the validity of the bounding procedure and an example based on real data is provided.

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