We define and study in this work a simple model allowing for a prudential valuation of solvency capital requirement while avoiding over-assessment specifically after market disruption. The main idea is to include a dampener component in charge of refining risk assessment after a market failure....

Market risk regulations adopted in response to recent crises aim to reduce financial risks. Nevertheless, a large number of practitioners feel that, if these rules seem to succeed in lowering volatility, they appear to rigidify the financial structure of the economic system and tend to increase...

The generalized multifractional Brownian motion (GMBM) is a continuous Gaussian process that extends the classical fractional Brownian motion (FBM) and multifractional Brownian motion (MBM) (SIAM Rev. 10 (1968) 422; INRIA Res. Rept. 2645 (1995); Rev. Mat. Iberoamericana 13 (1997) 19; Fractals: Theory...

Stochastic integration w.r.t. fractional Brownian motion (fBm) has raised strong interest in recent years, motivated in particular by applications in finance and Internet traffic modelling. Since fBm is not a semi-martingale, stochastic integration requires specific developments. Multifractional...

A lot is known about the Hölder regularity of stochastic processes, in particular in the case of Gaussian processes. Recently, a finer analysis of the local regularity of functions, termed 2-microlocal analysis, has been introduced in a deterministic frame: through the computation of the...