function IP = HARAIPvalue(X, XDistr, alpha, gama)
% Copyright (c) 2001-2009 by Ales Cerny
% usage HARAIPvalue(X, XDistr, alpha, gama)
% HARAIPvalue returns the value of investment potential for a normalized 
% HARA utility with shape parameter gama. Alpha represents a (not 
% necessarily optimal) investment decision of an investor with unit local 
% risk aversion, facing a single risky investment with excess return X,
% distributed according to XDistr.

%************************************************************************%
% HARAIPvalue.m - supplementary program to                               %
% Ales Cerny (2009) Mathematical Techniques in Finance (2nd ed.)         % 
% Princeton University Press http://press.princeton.edu/titles/9079.html %
%************************************************************************%
    
% This code is provided 'as-is', without any express or implied warranty.  
% 
% Permission is granted to anyone to use this code for any purpose, 
% subject to the following restrictions:
% 
% 1. The origin of this code must not be misrepresented; you must not
%    claim that you wrote the original code.
% 2. Modified code versions must be plainly marked as such, and must not 
%    be misrepresented as being the original code.
% 3. This notice may not be removed from any source distribution.

% NOTICE TO STUDENTS: To avoid accusations of plagiarism, if you use this 
% code or its modifications in assessed work you should prepend it with a 
% note stating: 
%   "This is the original/modified version of the code HARAIPvalue.m by 
%    Ales Cerny (2009), Mathematical Techniques in Finance (2nd ed.),  
%    Princeton University Press. The original version is available from 
%    http://www.martingales.info/mtfweb2".
% A similar acknowledgement should appear prominently inside your written 
% report.

wealth = 1 + alpha'*X / gama;
u = (wealth.^(1-gama))*XDistr';
IP = gama*(u^(1/(1-gama))-1);