Pogojna tvegana vrednost in optimizacija portfeljev

delo diplomskega seminarja

Dejan Gašparič (Author), Damjana Kokol-Bukovšek (Mentor), Aleš Toman (Co-mentor)

Abstract

V delu diplomskega seminarja z naslovom Pogojna tvegana vrednost in optimizacija portfeljev je predstavljen pristop optimizacije portfelja na podlagi minimizacije mere tveganja portfelja, imenovane pogojna tvegana vrednost. Čeprav definicija omenjene mere tveganja sloni na definiciji mere tveganja, imenovane tvegana vrednost, pa vendarle velja, da tehnika pristopa optimizacije portfelja na podlagi minimizacije pogojne tvegane vrednosti portfelja ne potrebuje predhodne določitve vrednosti tvegane vrednosti portfelja. Optimizacija portfelja, natančneje deležev nenegativnih pozicij posameznih finančnih instrumentov v portfelju, se prevede na minimizacijo konveksne zvezno odvedljive funkcije, s pomočjo katere dobimo pripadajoči vrednosti pogojne tvegane vrednosti in tvegane vrednosti portfelja. Funkcija vsebuje integral skupne gostote verjetnosti donosnosti finančnih instrumentov. Za uporabo na konkretnih podatkih zato uporabimo eno izmed tehnik vzorčenja iz vrednosti tržnih spremenljivk za predpisani portfelj, s tem aproksimiramo prej omenjeni integral in optimizacijo prevedemo na problem linearnega programiranja.

Keywords

finančna matematika;optimizacija portfelja;upravljanje s tveganji;mera tveganja;koherentna mera tveganja;tvegana vrednost;pogojna tvegana vrednost;linearno programiranje;konveksna analiza;

Data

Language:	Slovenian
Year of publishing:	2018
Typology:	2.11 - Undergraduate Thesis
Organization:	UL EF - Faculty of Economics
Publisher:	[D. Gašparič]
UDC:	519.8
COBISS:	18412377
Views:	998
Downloads:	485
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Conditional value at risk and portfolios optimization
Secondary abstract:	In the diploma seminar thesis entitled Conditional Value at Risk and portfolios optimization, a portfolio optimization approach based on the minimization of the portfolio risk measure, called the Conditional Value at Risk, is presented. Although the definition of the above-mentioned risk measure is based on the definition of the risk measure, called the Value at Risk, the technique of the portfolio optimization approach based on minimization of the Conditional Value at Risk of the portfolio does not require the calculation of the Value at Risk of the portfolio beforehand. The optimization of the portfolio, more precisely, the shares of the non-negative positions in individual financial instruments in the portfolio, is transformed to the minimization of a convex and continuously differentiable function, through which the values of the Conditional Value at Risk and the Value at Risk of the portfolio are obtained. The function contains an integral of the joint probability density function of financial instruments returns. To use the approach on concrete data, we use one of the sampling techniques from the values of the portfolio related market variables, approximate the beforementioned integral and transform the optimization problem into the problem of linear programming.
Secondary keywords:	portfolio optimization;risk management;risk measure;coherent risk measure;value at risk;conditional value at risk;linear programming;convex analysis;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 1. stopnja
Pages:	27 str.
ID:	10949232