We propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semi-martingale log asset price process which is subject to noise and non-synchronous observations. The estimator is constructed based on a local average of block-wise parametric spectral covariance...

For a semi-martingale Xt, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation (X;X)t is constructed based on observations in the vicinity of Xt. The problem is embedded in a Poisson point process framework, which reveals an interesting connection to the theory...

We propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semi-martingale log asset price process which is subject to noise and non-synchronous observations. The estimator is constructed based on a local average of block-wise parametric spectral covariance...

We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to lead to an appropriate estimation for time-varying volatilities stems from an...

As a main step in the numerical solution of control problems in continous time, the controlled process is approximated by sequences of controlled Markov chains, thus discretizing time and space. A new feature in this context is to allow for delay in the dynamics. The existence of an optimal...

We present an explicit solution to an optimal stopping problem in a model described by a stochastic delay differential equation with an exponential delay measure. The model of proof is based on reducting the initial problem to a free-boundary problem and solving the latter by means of the...