The paper studies the impact of the sampling frequency on the volatility of financial time series. We suggest to model the dependence of volatility on sampling frequency via delay equations for the underlying prices. It appears that these equations allow to model the price processes with...

The paper studies methods of dynamic estimation of volatility for financial time series. We suggest to estimate the volatility as the implied volatility inferred from some artificial 'dynamically purified' price process that in theory allows to eliminate the impact of the stock price movements....

The paper addresses the forecasting of realised volatility for financial time series using the heterogeneous autoregressive model (HAR) and machine learning techniques. We consider an extended version of the existing HAR model with included purified implied volatility. For this extended model,...

The paper addresses the forecasting of realised volatility for financial time series using the heterogeneous autoregressive model (HAR) and machine learning techniques. We consider an extended version of the existing HAR model with included purified implied volatility. For this extended model,...

This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial processes, i.e., by processes with fixed size binary...

We consider a multi-stock continuous time incomplete market model with random coefficients. We study the investment problem in the class of strategies which do not use direct observations of the appreciation rates of the stocks, but rather use historical stock prices and an a priory given...

In Bender and Dokuchaev (2013), we studied a control problem related to swing option pricing in a general non-Markovian setting. The main result there shows that the value process of this control problem can be uniquely characterized in terms of a first order backward SPDE and a pathwise...

This paper studies the properties of discrete time stochastic optimal control problems associated with portfolio selection. We investigate if optimal continuous time strategies can be used effectively for a discrete time market after a straightforward discretization. We found that Merton's...

Backward stochastic partial differential equations of parabolic type in bounded domains are studied in the setting where the coercivity condition is not necessary satisfied and the equation can be degenerate. Some generalized solutions based on the representation theorem are suggested. In...

We investigate an optimal investment problem with a general performance criterion which, in particular, includes discontinuous functions. Prices are modeled as diffusions and the market is incomplete. We find an explicit solution for the case of limited diversification of the portfolio, i.e. for...