In this thesis, we are interested in the stochastic differential equation with jumps under regime switching. Firstly, we investigate a continuous-time version of the mean-variance portfolio selection model with jumps under regime switching. The portfolio selection proposed and analyzed for a market consisting of one bank account an d multiple stocks. The random regime switching is assumed to be independent of the underlying Brownian motion and jump processes. Secondly, we consider the problem of pricing contigent claims on a stock whose price process is modeled by a Levy process. Since the market is incomplete and there is not a unique equivalent martingale measure. We study approaches to pricing options. Finally, we investigate a continuous-time version Markowitz's mean-variance portfolio selection problem which is studied in a market with one bank account, one stock and proportional transaction costs. This is a singular stochastic control problem. Via a series of transformations, the problem is turned into a double obstacle problem.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:678345 |
| Date | January 2010 |
| Creators | Zhao, Lin |
| Publisher | Swansea University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://cronfa.swan.ac.uk/Record/cronfa42401 |
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