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Some Applications of Variational Inequalities in Mathematical Finance and Numerics

Dahlgren, Martin LU (2005)
Abstract
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Docent Tysk, Johan, Uppsala University
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Matematik, Mathematics, HJB quasi variational inequalities, option pricing, Impulse control, parabolic PDE, finite element method, Galerkin method
publisher
Centre for Mathematical Sciences, Lund University
defense location
MH:C
defense date
2005-01-21 13:15
ISSN
1404-0034
ISBN
91-628-6357-6
language
English
LU publication?
yes
id
59738de3-73db-46a0-84f5-7bf02ffd004a (old id 544101)
date added to LUP
2007-09-27 14:59:16
date last changed
2016-09-19 08:44:57
@phdthesis{59738de3-73db-46a0-84f5-7bf02ffd004a,
  abstract     = {This thesis contains two parts. The first part deals with a<br/><br>
<br/><br>
stochastic impulse control problem, subject to the restriction of<br/><br>
<br/><br>
a minimum time lapse in between interventions made by the<br/><br>
<br/><br>
controller. We prove existence of an optimal control and show that<br/><br>
<br/><br>
the value function of the control problem satisfies a system of<br/><br>
<br/><br>
quasi-variational inequalities. Furthermore, we apply the control<br/><br>
<br/><br>
method to price Swing options on the stock and commodity markets<br/><br>
<br/><br>
and to value a large position in a risky asset.<br/><br>
<br/><br>
In the second part we investigate a variational method for solving<br/><br>
<br/><br>
a class of linear parabolic partial differential equations. The<br/><br>
<br/><br>
method does not use time-stepping. The basic idea is to transform<br/><br>
<br/><br>
the non-coercive parabolic operators into equivalent coercive<br/><br>
<br/><br>
operators. We present one way to discretize the equations. We also<br/><br>
<br/><br>
give some numerical examples and results on convergence of the<br/><br>
<br/><br>
numerical scheme.},
  author       = {Dahlgren, Martin},
  isbn         = {91-628-6357-6},
  issn         = {1404-0034},
  keyword      = {Matematik,Mathematics,HJB quasi variational inequalities,option pricing,Impulse control,parabolic PDE,finite element method,Galerkin method},
  language     = {eng},
  publisher    = {Centre for Mathematical Sciences, Lund University},
  school       = {Lund University},
  title        = {Some Applications of Variational Inequalities in Mathematical Finance and Numerics},
  year         = {2005},
}