Functional approximation methods for solving stochastic control problems in finance
| dc.contributor.advisor | Tompaidis, Efstathios, 1967- | en |
| dc.contributor.committeeMember | Garlappi, Lorenzo | en |
| dc.contributor.committeeMember | Morton, David | en |
| dc.contributor.committeeMember | Muthuraman, Kumar | en |
| dc.contributor.committeeMember | Zariphopoulou, Thaleia | en |
| dc.creator | Yang, Chunyu, 1979- | en |
| dc.date.accessioned | 2010-12-02T20:53:04Z | en |
| dc.date.available | 2010-12-02T20:53:04Z | en |
| dc.date.available | 2010-12-02T20:53:11Z | en |
| dc.date.issued | 2010-08 | en |
| dc.date.submitted | August 2010 | en |
| dc.date.updated | 2010-12-02T20:53:11Z | en |
| dc.description | text | en |
| dc.description.abstract | I develop a numerical method that combines functional approximations and dynamic programming to solve high-dimensional discrete-time stochastic control problems under general constraints. The method relies on three building blocks: first, a quasi-random grid and the radial basis function method are used to discretize and interpolate the high-dimensional state space; second, to incorporate constraints, the method of Lagrange multipliers is applied to obtain the first order optimality conditions; third, the conditional expectation of the value function is approximated by a second order polynomial basis, estimated using ordinary least squares regressions. To reduce the approximation error, I introduce the test region iterative contraction (TRIC) method to shrink the approximation region around the optimal solution. I apply the method to two Finance applications: a) dynamic portfolio choice with constraints, a continuous control problem; b) dynamic portfolio choice with capital gain taxation, a high-dimensional singular control problem. | en |
| dc.description.department | Information, Risk, and Operations Management (IROM) | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.uri | http://hdl.handle.net/2152/ETD-UT-2010-08-1557 | en |
| dc.language.iso | eng | en |
| dc.subject | High-dimensional stochastic control problems | en |
| dc.subject | Dynamic portfolio choice | en |
| dc.subject | Approximations | en |
| dc.title | Functional approximation methods for solving stochastic control problems in finance | en |
| dc.type.genre | thesis | en |
| thesis.degree.department | Information, Risk, and Operations Management | en |
| thesis.degree.discipline | Information, Risk, and Operations Management | en |
| thesis.degree.grantor | University of Texas at Austin | en |
| thesis.degree.level | Doctoral | en |
| thesis.degree.name | Doctor of Philosophy | en |