One of the most famous problem of finding optimal weight to maximize an agent's expected terminal utility in finance literature is Merton's optimal portfolio problem. Classic solution to this problem is given by stochastic Hamilton-Jacobi-Bellman Equation where we briefly review it in chapter 1. Similar idea has found many applications in other finance literatures and we will focus on its application to the high-frequency trading using limit orders in this thesis. In [1], major analysis using the constant volatility arithmetic Brownian motion stock price model with exponential utility function is described. We re-analyze the solution of HJB equation in this case using different asymptotic expansion. And then, we extend the model to the regime-switching volatility model to capture the status of market more accurately.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/25636 |
| Date | 01 January 2011 |
| Creators | Jeon, Yoontae |
| Contributors | Jaimungal, Sebastian |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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