Nested Conditional Value-at-Risk portfolio selection: a model with temporal dependence driven by market-index volatility

We propose a multistage stochastic programming model to manage a multiperiod portfolio allocation problem. The optimization problem, formulated through the nested Conditional Value-at-Risk model, is characterized by an initial allocation date and by other dates where the portfolio may be reallocated. We describe asset log returns through a single-factor model where the driving factor is the market-index log return modelled by a Generalized Autoregressive Conditional Heteroskedasticity process to take into account the serial dependence usually observed. Under the assumption of zero transaction costs, we propose a backward induction scheme based on cubic spline interpolation to reduce the computational complexity of the problem and find an approximated solution to the optimization problem.