Global Asset Return in Pension Funds: a dynamical risk analysis

The aim of the paper is to develop a technique for rebalancing
pension fund portfolios in function of their pointwise level of risk.
The performance of pension funds is often measured by their global asset
returns because of the latter’s influence on periodic contributions and/or
future benefits. However, in periods of market crisis attention is focused
on the risk level given their social security (and not speculative) function.
We describe the process of the global asset return by a multifractional
Brownian motion using the function H(t) to detect high or low volatility
phases. A procedure is carried out to balance the asset composition
when the established local degree of risk is exceeded. The application is
carried out on portfolios obtained in accordance with Italian regulations
regarding investment limits.