Organization in finance prepared by stohastic differential equations with additive and nonlinear models and continuous optimization

Pakize Taylan (Author), Gerhard-Wilhelm Weber (Author)

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

podjetje;poslovne finance;optimiranje;matematični modeli;stohastični modeli;operacijsko raziskovanje;

Data

Language:	English
Year of publishing:	2008
Typology:	1.01 - Original Scientific Article
Organization:	UM FOV - Faculty of Organizational Sciences
Publisher:	Moderna organizacija
UDC:	005.591.1:519.863
COBISS:	244516864
ISSN:	1318-5454
Parent publication:	Organizacija
Views:	788
Downloads:	95
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary title:	Organizacija v financah izhajajoč iz stohasticnih diferencialnih enačb in nelinearnih modelov zvezne optimizacije
Secondary abstract:	Osrednji element v organizaciji finančnih sredstev, tako sredstev posameznika kot tudi podjetja ali družbene skupine, je oblikovanje, analiza in optimizacija portfelja. To zahteva modeliranje časovno spremenljivih procesov. Tako kot na mnoge procese v naravi, tehniki ali gospodarstvu tudi na finančne procese vplivajo naključne fluktuacije. Zato smo uporabili stohastične diferencialne enačbe, saj v realnosti, še posebej v finančnem sektorju, na mnoge procese vpliva naključni šum. Pomanjkljivost tega načina pa je, da je te enačbe težko predstaviti v obliki primerni za računalnik, in jih je težko reševati. V tem članku smo jih izrazili na poenostavljen način, tako, da smo uporabili aproksimacijo tako z diskretizacijo in kot tudi aditivnimi modeli, ki temeljijo na zlepkih. Določanje parametrov se nanaša na linearne koeficiente zlepkov in delno nelinearne probabilistične parametre. Izgradili smo penalizirano residualno vsoto kvadratov za ta model in obravnavali nelinearnosti, ki os se pojavljale, z Gauss-Newtonovo in Levenberg-Marquardt-ovo metodo za določanje iteracijskih korakov. Raziskovali smo tudi kdaj je s tem povezani program za minimizacijo lahko napisan kot Tikhonov problem regularizacije , in ga obravnavamo z uporabo zveznih optimizacijskih tehnik. Bolj natančno, pripravimo dostop do elegantnega okvirja koničnega kvadratnega programiranja. Ti konveksni optimizacijski problemi so zelo dobro strukturirani, zato so podobni linearnim programom, torej omogočajo uporabo metod interne točke.
Secondary keywords:	podjetje;poslovne finance;optimiranje;matematični modeli;stohastični modeli;operacijsko raziskovanje;
URN:	URN:NBN:SI
Type (COBISS):	Scientific work
Pages:	str. 185-193
Volume:	ǂLetn. ǂ41
Issue:	ǂšt. ǂ5
Chronology:	sep.-okt. 2008
DOI:	10.2478/v10051-008-0020-8
ID:	10896222