This article proposes an interest rate model ruled by mean reverting Lévy processes with a sub-exponential memory of their sample path. This feature is achieved by considering an Ornstein-Uhlenbeck process in which the exponential decaying kernel is replaced by a Mittag-Leffler function. Based...

This paper develops a new version of the Hull-White's model of interest rates, in which the volatility of the short term rate is driven by a Markov switching multifractal model. The interest rate dynamics is still mean reverting but the constant volatility of the Brownian motion is replaced by a...

This paper addresses the problem of dynamic asset allocation under a bounded shortfall risk in a market composed of three assets: cash, stocks and a zero coupon bond. The dynamics of the instantaneous short rates is driven by a Hull and White model. In this setting, we determine and compare...

We propose an interest rate model driven by a particular Lévy Process, the normal inverse Gaussian (NIG) process, in which the SDE chosen to govern the evolution of the short term rate is directly inspired from the Hull & White model. The interest rate dynamics is still mean reverting but the...