Title: Model reduction and filtering for portfolio optimization in hidden Markov models
Authors: Joern Sass - University of Kaiserslautern (Germany) [presenting]
Abstract: A regime switching model, where the observation process is a diffusion process whose drift and volatility coefficients jump governed by a continuous-time Markov chain, can explain some of the stylized facts of asset returns. In the special case that the volatility is constant, the underlying Markov chain can no longer be observed and has to be estimated by its filter. Portfolio decisions then depend on this filter and its dynamics. In fact it turns out that optimal portfolio policies and filter equations rely on the same signal to noise matrix. This can be used to reduce the dimension of the model to the dimension of this matrix if it has full rank. The eigenvalues of this matrix then provide a way to decompose the optimal portfolio in investments in mutual funds. In contrast to classical mutual fund theorems in continuous time, their composition is constant over time but the optimal policy is not. We provide convergence and decomposition results for optimization and filtering. Further we analyze the case of signal to noise matrices which are not of full rank and look at extensions to regime switching models and to hidden Markov models with non-constant volatility. We discuss consistency of the corresponding discrete-time and continuous-time models in view of filtering and portfolio optimization.