In this thesis, we consider the problem of continuous-time stochastic control with full and partial information and quadratic costs. Under some assumptions we reduce the problem of controlling a general diffusion process into controlling a piecewise linear system, called the Linearized system. The Linearized system is defined with respect to a time-partition of the fixed horizon [0,T]. We initially prove that the cost functional associated with the Linearized system converges to the cost functional of the original system as the mesh of the partition goes to 0. This in turn implies that an optimal control for the approximating system is also ε-optimal for the original system. Hence we centre our analysis at obtaining the optimal control for the Linearized system. To this end, we present two methodologies : the Perturbation method and the Policy Improvement method. In the first method, by imposing boundedness assumptions on the coefficients of the controlled diffusion, we construct the optimal control in each subinterval of the partition based on the framework of the so-called Linear Quadratic Regulator problem. In the second method we construct the optimal control in each subinterval of the partition by using a criterion under which, by starting from an arbitrary control and an associated cost, we eventually obtain, after consecutive steps, the control which minimises the cost functional of the Linearized system.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:702812 |
| Date | January 2016 |
| Creators | Kollias-Liapis, Spyridon |
| Contributors | Crisan, Dan |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/43756 |
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