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 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 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...

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