Abstract: A system and computer-implemented method for generating random vectors for estimating portfolio risk is provided. Historical financial variable data of financial assets is stored in a memory. Parameters of a copula are estimated. Random vectors are generated from the copula. Risk for the financial assets is calculated based on the random vectors.

Abstract: A system and method for providing reallocation and reverse optimization of a financial portfolio using a parametric leptokurtic distribution are provided. A time series including risk factors applicable over at least one time horizon, a portfolio including financial assets, a quantile, and one or more risk adjusted return points for the financial assets is stored. The financial assets are associated with the risk factors. A subordinated parametric distribution model exhibiting leptokurtic behavior is generated. A function of expected tail loss for the quantile based on the subordinated parametric distribution model exhibiting leptokurtic behavior is expressed. A set of portfolio asset weight changes for each of the financial assets is determined based on the expected tail loss at each such time horizon and for each risk adjusted return point. Reallocation of the portfolio is provided based on the portfolio asset weight changes for each risk adjusted return point for the portfolio.

Abstract: A system and method for providing reallocation and reverse optimization of a financial portfolio using a parametric leptokurtic distribution are provided. A time series including risk factors applicable over at least one time horizon, a portfolio including financial assets, a quantile, and one or more risk adjusted return points for the financial assets is stored. The financial assets are associated with the risk factors. A subordinated parametric distribution model exhibiting leptokurtic behavior is generated. A function of expected tail loss for the quantile based on the subordinated parametric distribution model exhibiting leptokurtic behavior is expressed. A set of portfolio asset weight changes for each of the financial assets is determined based on the expected tail loss at each such time horizon and for each risk adjusted return point. Reallocation of the portfolio is provided based on the portfolio asset weight changes for each risk adjusted return point for the portfolio.

Abstract: A system and method for providing optimization of a financial portfolio using a parametric leptokurtic distribution is presented. One or more risk factors associated with a plurality of financial assets maintained in a portfolio and applicable over at least one time horizon are provided. A subordinated parametric distribution model having leptokurtic behaviors is specified for the risk factors with a measurement of risk expressed as a function of expected tail loss for a significance level or quantile. The subordinated distribution model is applied at each such time horizon to determine a distribution of the risk factors for the financial assets. Portfolio weights providing a substantially maximum risk adjusted return for the portfolio are determined.