Essays of the dynamic portfolio choice Defended on Friday, 6 October 2006
This thesis deals with the subject of dynamic optimal portfolio choice. In the first two chapters we consider the problem usually encountered in the unconstrained portfolio choice, namely the hedging against adverse changes of state variables. In this context we focus on the interest rate risk hedging. We analyze the problem in question in both continuous and discrete time by applying the martingale approach to the optimal portfolio choice combined with Malliavin calculus. In the continuous time framework we provide an alternative derivation of optimal portfolio policies in the chosen model of financial markets and confirm the convergence of optimal portfolio policies simulated according to the Malliavin calculus method to their continuous-time counterparts. In the discrete time we confirm several properties of the optimal portfolios known from the continuous time analysis. Properties, which are not intuitive enough in continuous time are analyzed in the discrete time in more detail. The last two chapters are devoted to the problem of constrained portfolio choice. We investigate the problem of asset and liability management in the defined-benefit pension scheme with a stochastic liability. In the simulation exercise we compare the performance of several dynamic portfolio strategies against one another and fixed mixes in both complete and incomplete financial markets. We conclude that dynamic strategies are not superior to fixed mixes. The last part of this thesis covers an empirical investigation of constant proportion portfolio insurance (CPPI) strategies, for which theoretical properties are well known in the literature. We compare the theory against empirical results and CPPI against the alternative portfolio insurance strategy.
Dynamic optimal portfolio choice, martingale approach, Malliavin calculus, interest rate risk hedging, asset liability management, pension schemes, constant proportion portfolio insurance