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Adapted Downhill Simplex Method for Pricing Convertible Bonds
Mälardalens högskola, Institutionen för matematik och fysik. (Mathematics/Applied Mathematics)
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation. (Mathematics/Applied Mathematics)ORCID-id: 0000-0002-0139-0747
2007 (Engelska)Ingår i: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 13, nr 4, s. 130-147Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

The paper is devoted to modeling optimal exercise strategies of thebehavior of investors and issuers working with convertible bonds.This implies solution of the problems of stock price modeling, payoffcomputation and minimax optimization.Stock prices (underlying asset) were modeled under the assumptionof the geometric Brownian motion of their values. The Monte Carlomethod was used for calculating the real payoff which is the objectivefunction. The minimax optimization problem was solved using thederivative-free Downhill Simplex method.The performed numerical experiments allowed to formulate recommendationsfor the choice of appropriate size of the initial simplex inthe Downhill Simplex Method, the number of generated trajectoriesof underlying asset, the size of the problem and initial trajectories ofthe behavior of investors and issuers.

Ort, förlag, år, upplaga, sidor
2007. Vol. 13, nr 4, s. 130-147
Nationell ämneskategori
Beräkningsmatematik
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
URN: urn:nbn:se:mdh:diva-4225OAI: oai:DiVA.org:mdh-4225DiVA, id: diva2:121266
Tillgänglig från: 2008-04-28 Skapad: 2008-04-28 Senast uppdaterad: 2013-12-02Bibliografiskt granskad
Ingår i avhandling
1. Numerical Algorithms for Optimization Problems in Genetical Analysis
Öppna denna publikation i ny flik eller fönster >>Numerical Algorithms for Optimization Problems in Genetical Analysis
2008 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
Abstract [en]

The focus of this thesis is on numerical algorithms for efficient solution of QTL analysis problem in genetics.

Firstly, we consider QTL mapping problems where a standard least-squares model is used for computing the model fit. We develop optimization methods for the local problems in a hybrid global-local optimization scheme for determining the optimal set of QTL locations. Here, the local problems have constant bound constraints and may be non-convex and/or flat in one or more directions. We propose an enhanced quasi-Newton method and also implement several schemes for constrained optimization. The algorithms are adopted to the QTL optimization problems. We show that it is possible to use the new schemes to solve problems with up to 6 QTLs efficiently and accurately, and that the work is reduced with up to two orders magnitude compared to using only global optimization.

Secondly, we study numerical methods for QTL mapping where variance component estimation and a REML model is used. This results in a non-linear optimization problem for computing the model fit in each set of QTL locations. Here, we compare different optimization schemes and adopt them for the specifics of the problem. The results show that our version of the active set method is efficient and robust, which is not the case for methods used earlier. We also study the matrix operations performed inside the optimization loop, and develop more efficient algorithms for the REML computations. We develop a scheme for reducing the number of objective function evaluations, and we accelerate the computations of the derivatives of the log-likelihood by introducing an efficient scheme for computing the inverse of the variance-covariance matrix and other components of the derivatives of the log-likelihood.

Ort, förlag, år, upplaga, sidor
Västerås: Mälardalens högskola, 2008
Serie
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 59
Nyckelord
Quantitative Trait Loci (QTL), restricted maximum likelihood (REML), variance components, average information (AI) matrix, Local optimization, Quasi-Newton method, Active Set method, Hessian approximation, BFGS update
Nationell ämneskategori
Beräkningsmatematik
Forskningsämne
Matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-650 (URN)978-91-85485-84-0 (ISBN)
Disputation
2008-06-05, Kappa, U, Högskoleplan 1, Västerås, 13:00
Opponent
Handledare
Tillgänglig från: 2008-04-28 Skapad: 2008-04-28

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Malyarenko, Anatoliy

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Beräkningsmatematik

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