13 Aprile, 2016 16:00

Sezione di Finanza Quantitativa

Recent results on (quasiconvex) risk measures and related portfolio optimization problems

Elisa Mastrogiacomo, dipartimento di statistica e metodi quantitativi - Università di Milano Bicocca

Aula Seminari III piano

The main goal of this talk is to present some recent results concerning the study of (quasiconvex) risk measures and related portfolio optimization problems both from a theoretical and numerical point of view.
The first (theoretical) problem that we are going to present is the characterization of Pareto optimal allocations for quasiconvex risk measures. Following the approach of Jouini et al. (2008) for convex risk measures, in the quasiconvex case we investigate the notions of (weakly) Pareto optimality and of exactness of the so-called quasiconvex inf-convolution as well as existence for weakly Pareto optimal allocations. Moreover, we give a necessary condition for weakly optimal risk sharing that is also sufficient under cash-additivity of at least one between the risk measures.
The second problem concerns with the study of optimal portfolio allocation strategies under cumulative prospect theory (CPT), both from a theoretical and empirical point of view. Our aim is twofold. First, we exhibit the impact of higher-moments and CPT parameters on suitable Mean/Risk efficient frontier. On a second stage, we investigate empirically, for different portfolios, the optimal choice problem
for an investor who behaves according to the CPT, considering different parameters for this utility function. We then compare our empirical results with the Mean Variance (MV) and the Global Minimum Variance (GMV) portfolios, from an in-sample and out-of-sample perspective.
Finally we will concentrate on a portfolio optimization problem under state-dependent expected utility. Inspired by the recent results in Bjork, Murgoci and Zhou (2014), we analyze the mean–variance portfolio selection problem with state-dependent risk aversion. We consider a continuous time Lévy model consisting of two assets, one stock price with dynamics of jump-type and a bank account with constant risk-free rate. Since this problem is time inconsistent we approach it within a
game theoretic setting and look for subgame perfect Nash equilibrium strategies. We show that, under this approach an extension of the standard dynamic programming equation to a system of nonlinear PDEs is needed.