Some Applications of Variational Inequalities in Mathematical Finance and Numerics

Martin Dahlgren

Forskningsoutput: AvhandlingDoktorsavhandling (sammanläggning)

Sammanfattning

This thesis contains two parts. The first part deals with a

stochastic impulse control problem, subject to the restriction of

a minimum time lapse in between interventions made by the

controller. We prove existence of an optimal control and show that

the value function of the control problem satisfies a system of

quasi-variational inequalities. Furthermore, we apply the control

method to price Swing options on the stock and commodity markets

and to value a large position in a risky asset.

In the second part we investigate a variational method for solving

a class of linear parabolic partial differential equations. The

method does not use time-stepping. The basic idea is to transform

the non-coercive parabolic operators into equivalent coercive

operators. We present one way to discretize the equations. We also

give some numerical examples and results on convergence of the

numerical scheme.
Originalspråkengelska
KvalifikationDoktor
Tilldelande institution
  • Matematik LTH
Handledare
  • Fontes, Magnus, handledare
Tilldelningsdatum2005 jan. 21
Förlag
ISBN (tryckt)91-628-6357-6
StatusPublished - 2005

Bibliografisk information

Defence details

Date: 2005-01-21
Time: 13:15
Place: MH:C

External reviewer(s)

Name: Tysk, Johan
Title: Docent
Affiliation: Uppsala University

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Ämnesklassifikation (UKÄ)

  • Matematik

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