dc.contributor.author | Ma, Kai | |
dc.date.accessioned | 2015-12-03 16:39:29 (GMT) | |
dc.date.available | 2015-12-03 16:39:29 (GMT) | |
dc.date.issued | 2015-12-03 | |
dc.date.submitted | 2015-11-25 | |
dc.identifier.uri | http://hdl.handle.net/10012/10029 | |
dc.description.abstract | In this thesis, we focus on solving multidimensional HJB equations which are derived from
optimal stochastic control problems in the financial market. We develop a fully implicit,
unconditionally monotone finite difference numerical scheme. Consequently, there are no
time step restrictions due to stability considerations, and the fully implicit method has
essentially the same complexity per step as the explicit method. The main difficulty in
designing a discretization scheme is development of a monotonicity preserving approximation
of cross derivative terms in the PDE. We primarily use a wide stencil based on a local
coordination rotation. The analysis rigorously show that our numerical scheme is $l_\infty$ stable,
consistent in the viscosity sense, and monotone. Therefore, our numerical scheme guarantees
convergence to the viscosity solution.
Firstly, our numerical schemes are applied to pricing two factor options under an uncertain
volatility model. For this application, a hybrid scheme which uses the fixed point stencil
as much as possible is developed to take advantage of its accuracy and computational efficiency.
Secondly, using our numerical method, we study the problem of optimal asset
allocation where the risky asset follows stochastic volatility. Finally, we utilize our numerical
scheme to carry out an optimal static hedge, in the case of an uncertain local volatility
model. | en |
dc.language.iso | en | en |
dc.publisher | University of Waterloo | en |
dc.title | Numerical Solutions of Two-factor Hamilton-Jacobi-Bellman Equations in Finance | en |
dc.type | Doctoral Thesis | en |
dc.pending | false | |
uws-etd.degree.department | David R. Cheriton School of Computer Science | en |
uws-etd.degree.discipline | Computer Science | en |
uws-etd.degree.grantor | University of Waterloo | en |
uws-etd.degree | Doctor of Philosophy | en |
uws.contributor.advisor | Forsyth, Peter | |
uws.contributor.affiliation1 | Faculty of Mathematics | en |
uws.published.city | Waterloo | en |
uws.published.country | Canada | en |
uws.published.province | Ontario | en |
uws.typeOfResource | Text | en |
uws.peerReviewStatus | Unreviewed | en |
uws.scholarLevel | Graduate | en |