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Organization in finance prepared by stohastic differential equations with additive and nonlinear models and continuous optimization
Pakize Taylan, Gerhard-Wilhelm Weber, 2008, original scientific article

Abstract: A central element in organization of financal means by a person, a company or societal group consists in the constitution, analysis and optimization of portfolios. This requests the time-depending modeling of processes. Likewise many processes in nature, technology and economy, financial processes suffer from stochastic fluctuations. Therefore, we consider stochastic differential equations (Kloeden, Platen and Schurz, 1994) since in reality, especially, in the financial sector, many processes are affected with noise. As a drawback, these equations are hard to represent by a computer and hard to resolve. In our paper, we express them in simplified manner of approximation by both a discretization and additive models based on splines. Our parameter estimation refers to the linearly involved spline coefficients as prepared in (Taylan and Weber, 2007) and the partially nonlinearly involved probabilistic parameters. We construct a penalized residual sum of square for this model and face occuring nonlinearities by Gauss-Newton's and Levenberg-Marquardt's method on determining the iteration step. We also investigate when the related minimization program can be written as a Tikhonov regularization problem (sometimes called ridge regression), and we treat it using continuous optimization techniques. In particular, we prepare access to the elegant framework of conic quadratic programming. These convex optimation problems are very well-structured, herewith resembling linear programs and, hence, permitting the use of interior point methods (Nesterov and Nemirovskii, 1993).
Keywords: stochastic differential equations, regression, statistical learning, parameter estimation, splines, Gauss-Newton method, Levenberg-Marquardt's method, smoothing, stability, penalty methods, Tikhonov regularization, continuous optimization, conic quadratic programming
Published in DKUM: 10.01.2018; Views: 1237; Downloads: 137
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Use of genetic algorithm for fitting Sovova's mass transfer model
Dejan Hrnčič, Marjan Mernik, Maša Knez Marevci, 2010, original scientific article

Abstract: A genetic algorithm with resizable population has been applied to the estimation of parameters for Sovovaćs mass transfer model. The comparison of results between a genetic algorithm and a global optimizer from the literatureshows that a genetic algorithm performs as good as or better than a global optimizer on a given set of problems. Other benefits of the genetic algorithm, for mass transfer modeling, are simplicity, robustness and efficiency.
Keywords: Sovova's mass transfer model, genetic algorithm, parameter estimation
Published in DKUM: 31.05.2012; Views: 1764; Downloads: 73
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