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Author:Leppänen, Samuli
Title:Numerical Methods in Risk Minimization
Numeeriset menetelmät riskin minimointitehtävissä
Publication type:Master's thesis
Publication year:2009
Pages:46 (+5)      Language:   eng
Department/School:Matematiikan ja systeemianalyysin laitos
Main subject:Matematiikka   (Mat-1)
Supervisor:Valkeila, Esko
Instructor:Pennanen, Teemu
OEVS:
Electronic archive copy is available via Aalto Thesis Database.
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Location:P1 Ark T80     | Archive
Keywords:risk minimization
convex optimization
optimized certainty equivalent
saddle point problem
variational inequality
large scale optimization
hedging problem
riskin minimointi
konveksi optimointi
optimoitu varmuusekvivalentti
satulapistetehtävä
variaatioepäyhtälö
suurien tehtävien numeerinen optimointi
portfolionsuojaustehtävä
Abstract (eng): In this thesis numerical methods in risk minimization for a class of risk measures is considered.
We represent risk measures using optimized certainty equivalent and use the representation to formulate a saddle point problem corresponding a problem of risk minimization.
The representation is used to discretize the problem.
We study three simple subgradient algorithms for nonsmooth convex optimization.
Some theoretical background of convex analysis and integral functionals is briefly reviewed.
In numerical experiments we test the performance of the algorithms on a hedging problem.
Abstract (fin): Työssä käsitellään numeerisia menetelmiä riskin minimointitehtävässä eräälle riskimittojen luokalle.
Riskimitat esitetään käyttäen optimoitua varmuusekvivalenttia ja tämän esityksen avulla muodostetaan riskin minimointitehtävää vastaava satulapistetehtävä.
Esitystä käytetään myös tehtävän diskretointiin.
Työssä tutkitaan myös kolmea yksinkertaista aligradienttialgoritmia epäsileille konvekseille tehtäville.
Konveksin analyysin, integraalifunktionaalien ja stokastiikan teoriaa käydään läpi lyhyesti.
Algoritmien toimivuutta testataan portfolionsuojaustehtävässä.
ED:2009-11-25
INSSI record number: 38614
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