We examined the impact of including sustainability-related constraints in optimal portfolio decision-making. Our analysis covered an investment set containing the components of the S&P500 index from 1993 to 2008. Optimizations were performed according to the classic mean--variance approach,...

Let Mt be a vector martingale and <M>t denote its predictable quadratic variation. In this paper we present a bound for the probability that with a fixed vector z and discuss some of its applications to statistical estimation in autoregressive and linear diffusion models. Our approach is...</m>

In this paper we carry over the concept of reverse probabilistic representations developed in Milstein, Schoenmakers, Spokoiny [G.N. Milstein, J.G.M. Schoenmakers, V. Spokoiny, Transition density estimation for stochastic differential equations via forward-reverse representations, Bernoulli 10...

Summury In this note we consider the problem of confidence estimation of the covariance function of a stationary or locally stationary zero mean Gaussian process. The constructed confidence intervals are based on the usual empirical covariance estimate and a special estimate of its variance. The...

The paper is concerned with the problem of variance estimation for a high-dimensional regression model. The results show that the accuracy n-1/2 of variance estimation can be achieved only under some restrictions on smoothness properties of the regression function and on the dimensionality of...

Over recent years, a study on risk management has been prompted by the Basel committee for regular banking supervisory. There are however limitations of some widely-used risk management methods that either calculate risk measures under the Gaussian distributional assumption or involve numerical...

Numerical algorithms for the efficient pricing of multidimensional discrete-time American and Bermudan options are constructed using regression methods and a new approach for computing upper bounds of the options' price. Using the sample space with payoffs at optimal stopping times, we propose...

We consider the possibility of optimal choice of observation window in the problem of parameter estimation by the observations of an inhomogeneous Poisson process. A minimax lower bound is proposed for the risk of estimation under an arbitrary choice of observation window. Then the adaptive...