We develop a simple and general method for solving non-linear Hamilton-Jacobi-Bellman partial differential equations HJB PDEs. We apply our method to the portfolio model.

We present new stochastic differential equations, that are more general and simpler than the existing Ito-based stochastic differential equations. As an example, we apply our approach to the investment (portfolio) model.

We present a new simple method of estimating stochastic volatility and its volatility. This method is applicable to both cross-sectional and time-series data. Moreover, this method does not require volatility data series.