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Full-Text Articles in Physical Sciences and Mathematics
Fast Fifth-Order Polynomial Transforms For Generating Univariate And Multivariate Nonnormal Distributions, Todd C. Headrick
Fast Fifth-Order Polynomial Transforms For Generating Univariate And Multivariate Nonnormal Distributions, Todd C. Headrick
Todd Christopher Headrick
A general procedure is derived for simulating univariate and multivariate nonnormal distributions using polynomial transformations of order five. The procedure allows for the additional control of the fifth and sixth moments. The ability to control higher moments increases the precision in the approximations of nonnormal distributions and lowers the skew and kurtosis boundary relative to the competing procedures considered. Tabled values of constants are provided for approximating various probability density functions. A numerical example is worked to demonstrate the multivariate procedure. The results of a Monte Carlo simulation are provided to demonstrate that the procedure generates specified population parameters and …
Optimal Policies For Investment With Time-Varying Return Distributions, Douglas Steigerwald, Doncho Donchev, Svetlozar Rachev
Optimal Policies For Investment With Time-Varying Return Distributions, Douglas Steigerwald, Doncho Donchev, Svetlozar Rachev
Douglas G. Steigerwald
We develop a model in which investors must learn the distribution of asset returns over time. The process of learning is made more difficult by the fact that the distributions are not constant through time. We consider risk-neutral investors who have quadratic utility and are selecting between two risky assets. We determine the time at which it is optimal to update the distribution estimate and, hence, alter portfolio weights. Our results deliver an optimal policy for asset allocation, that is, the sequence of time intervals at which it is optimal to switch between assets, based on stochastic optimal control theory. …