# parmautility-methods: Utility Based Optimization In parma: Portfolio Allocation and Risk Management Applications

## Description

Utility based portfolio optimization using either Taylor series expansion of utility function with moments or scenario based.

## Usage

 ```1 2 3``` ```parmautility(U = c("CARA", "Power"), method = c("moment", "scenario"), scenario = NULL, M1 = NULL, M2 = NULL, M3 = NULL, M4 = NULL, RA = 1, budget = 1, LB = rep(0, length(M1)), UB = rep(1, length(M1))) ```

## Arguments

 `U` The utility function (only CARA curretly implemented). `method` Whether to use moment or scenario based optimization (only moment currently implemented). `scenario` A n-by-m scenario matrix. `M1` A vector (m) of forecasts. `M2` An m-by-m positive definite covariance matrix. `M3` An m-by-m^2 third co-moment matrix. `M4` An m-by-m^3 fourth co-moment matrix. `RA` Risk Aversion Coefficient for CARA. `budget` The investment constraint. `LB` The lower bounds for the asset weights (positive). `UB` The upper bounds for the asset weights.

## Details

The function currently only implements the CARA moment based approach, but will be expanded in the future. The moment approach can take as inputs either M1 and M2 (2-moment approximation), or M1, M2, M3 and M4 (4-moment approximation). Not many models generate M3 and M4, but the “gogarch” model with manig or magh distribution will.

## Value

A `parmaPort` object containing details of the PARMA optimized portfolio.

Alexios Ghalanos

## References

Ghalanos, A. and Rossi, E. and Urga, G. 2012, Independent Factor Autoregressive Conditional Density Model submitted-TBA

parma documentation built on May 29, 2017, 5:53 p.m.