The mean-field stochastic differential equation (MFSDE) has found various applications in science and engineering. Here, we investigate a class of MFSDE with jumps, governed by a finite dimensional Brownian motion and a Poisson random measure. We study large deviation estimates of its path...

When analysing the volatility related to high frequency financial data, mostly non-parametric approaches based on realised or bipower variation are applied. This article instead starts from a continuous time diffusion model and derives a parametric analog at high frequency for it, allowing...

When analysing the volatility related to high frequency financial data, mostly non-parametric approaches based on realised or bipower variation are applied. This article instead starts from a continuous time diffusion model and derives a parametric analog at high frequency for it, allowing...

When analysing the volatility related to high frequency financial data, mostly non-parametric approaches based on realised or bipower variation are applied. This article instead starts from a continuous time diffusion model and derives a parametric analog at high frequency for it, allowing...

When analysing the volatility related to high frequency financial data, mostly non-parametric approaches based on realised or bipower variation are applied. This article instead starts from a continuous time diffusion model and derives a parametric analog at high frequency for it, allowing...

We investigate within a continuous time setting how Knightian uncertainty characterized by k-ignorance affects the optimal timing policies of a risk-neutral and uncertainty averse investor in the case where the exercise payoff is monotonic. We prove that increased Knightian uncertainty...

This paper considers interest rate term structure models in a market attracting both continuous and discrete types of uncertainty. The event driven noise is modelled by a Poisson random measure. Using as numeraire the growth optimal portfolio, interest rate derivatives are priced under the...

Using a simple integral identity, we derive general expressions for the Laplace transform of the transition density of the process, if killing or reflecting boundaries are specified. We also obtain a number of useful expressions for the Laplace transforms of some functions of first-passage times...

We investigate within a continuous time setting how Knightian uncertainty characterized by k-ignorance affects the optimal timing policies of a risk-neutral and uncertainty averse investor in the case where the exercise payoff is monotonic. We prove that increased Knightian uncertainty...