Portfolio Optimization Under Multiscale Stochastic Volatility
Author | : Keqin Gong |
Publisher | : |
Total Pages | : 84 |
Release | : 2013 |
ISBN-10 | : 1303151553 |
ISBN-13 | : 9781303151552 |
Rating | : 4/5 (53 Downloads) |
Book excerpt: In this thesis, the classical Merton problem, a portfolio selection problem, is extended using multiscale volatility model which assumes that volatility of stock price depends on a fast scale process and a slow scale process. The Dynamic Programming Principle is used to establish the Hamilton-Jacobi-Bellman equation. An asymptotic method based on two small parameters from two scale factors, is applied in solving the equation to obtain an approximation of optimal trading strategy and value function, which is the expectation of utility of wealth in future. We also prove that when these two parameters are small, the error of our approximation of value function is small. Furthermore, we consider the counterparty risk in the portfolio selection problem, which means stock price has a jump at the default time and the stock is still tradable after default happens. In this scenario, an approximation of value function and optimal trading strategy is also derived and error of the approximation is estimated. Finally we use finite difference method to solve the problem and show how multiscale volatility model and counterparty default affect the results.