Dottorato in MODELLI PER L'ECONOMIA E LA FINANZA

Titolo della tesi: Dynamic portfolio optimization with stochastic investment opportunities and discontinuities

The present dissertation analyzes dynamic portfolio optimization problems with investment opportunities under different market scenarios. The portfolio allocation is based on decision-making to determine how many resources should allocated among various possible investments. It is well known that realistic portfolio choices must reflect the peculiarities of financial markets and economic agents; we use optimal control theory to replicate both economic investor behaviours and expected utility maximization. The novelty with respect to the existing literature lies in modelling precision instead of volatility, understood as the reciprocal of volatility, where both the stock and the state variables are subject to discontinuities. Such a non-affine structure guarantees a closed-form expression for the optimal weights for the financial assets involved in every different market setting. The optimal allocation result to be genuinely dynamic, consistent with Markowitz's well-known economic intuition that an inverse dependence of portfolio exposures on variance parameters should be observed. We consider several assumptions regarding investor preferences and market set-up. Empirical evidence shows that the investor is not only risk averse but also ambiguity averse. We attempt to provide a unifying approach to portfolio choice problems by studying a robust, dynamic, continuous-time optimal consumption and portfolio allocation problem for investors with recursive preferences who have access to both stock and derivatives markets.