The important application of semi-static hedging in financial markets naturally leads to the notion of conditionally quasi self-dual processes which is, for continuous semimartingales, related to conditional symmetry properties of both their ordinary as well as their stochastic logarithms. We...

We prove a stochastic maximum principle for controlled processes X(t)=X(u)(t) of the formdX(t)=b(t,X(t),u(t)) dt+[sigma](t,X(t),u(t)) dB(H)(t),where B(H)(t) is m-dimensional fractional Brownian motion with Hurst parameter . As an application we solve a problem about minimal variance hedging in...

Motivated by empirical evidence of long range dependence in macroeconomic variables like interest rates we propose a fractional Brownian motion driven model to describe the dynamics of the short and the default rate in a bond market. Aiming at results analogous to those for affine models we...