Some Applications of Variational Inequalities in Mathematical Finance and Numerics
(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:
https://lup.lub.lu.se/record/544101
- author
- Dahlgren, Martin LU
- supervisor
- opponent
-
- Docent Tysk, Johan, Uppsala University
- organization
- publishing date
- 2005
- 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 13:15:00
- ISBN
- 91-628-6357-6
- language
- English
- LU publication?
- yes
- id
- 59738de3-73db-46a0-84f5-7bf02ffd004a (old id 544101)
- date added to LUP
- 2016-04-01 16:35:30
- date last changed
- 2018-11-21 20:42:36
@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}},
keywords = {{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}},
}