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.

We present a new method of estimating the asset stochastic volatility and return. In doing so, we overcome some of the limitations of the existing random walk models, such as the GARCH/ARCH models.

We present a new model of forward dynamic utilities. In doing so, we provide unique (viscosity) solutions. In addition, we introduce Hausdorff-continuous viscosity solutions to the portfolio model.

We devise an estimation methodology which allows preferences estimation and comparative statics analysis without a reliance on Taylor’s approximations and the indirect utility function.

We introduce a new utility-based approach to pricing European and American options. In so doing, we overcome some of the limitations of the existing models.