The aim of this article is to show a simple way to construct asymptotic minimax lower bounds for risks based on different types of quadratic loss functions in semiparametric inference problems. For the sake of clarity, we consider the simple case of the state estimation of a dynamical system...

This paper tailors Monte Carlo simulations to the scope of binary options whose underlying dynamics obey jump-diffusion or jump-mean-reverting processes and may not be traded. In the process, the existence of well-defined arbitrage prices is justified notwithstanding a framework of incomplete...

The aim of this article is to show a simple way to construct asymptotic minimax lower bounds for risks based on different types of quadratic loss functions in semiparametric inference problems. For the sake of clarity, we consider the simple case of the state estimation of a dynamical system...

This paper discusses extensions of the implied diffusion approach of Dupire (1994) to asset processes with Poisson jumps. We show that this extension yields important model improvements, particularly in the dynamics of the implied volatility surface. The paper derives a forward PIDE...