%   Copyright (c) 2001-2009 by Ales Cerny

%************************************************************************%
% chapter4exe4.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 chapter4exe4.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.

% One period optimal investment with CRRA utility, incomplete markets, two
% risky asset, one year horizon.

clear;
clc

%*******************%
%    parameters     %
%*******************%
outputflag = 1;                  % 1 output should be printed, 0 nothing be printed. 
IPTolerance = 10^(-6);

gama=5;
Risky1 = [-0.2 -0.2  0.2  0.2];
Risky2 = [-0.1  0.2 -0.1  0.2];
XDistr = [0.125  0.125  0.375  0.375];
RiskFreeRate = 0.02;
X = [(Risky1-RiskFreeRate) ; (Risky2-RiskFreeRate)];

% quadratic utility calculations 
EX     = X*XDistr';                             % E[X] 
OmegaX = (X.*(ones(size(X,1),1)*XDistr))*X';    % OmegaX=E[XX']
SigmaX = OmegaX - EX*EX';                       % SigmaX = E[XX']-E[X]E[X]' 
[IP,beta]= HARAmax(X,XDistr,gama,IPTolerance,outputflag); 

disp(' ');
disp(sprintf('HARA investment potential     %12.4f            ', IP)); 
disp(sprintf('QU   investment potential     %12.4f            ', 1-sqrt(1/(1+EX'*(SigmaX\EX))))); 
disp(sprintf('%s',['HARA alpha                          ' num2str(beta'/gama,'%12.4f')]));                
disp(sprintf('%s',['QU   alpha                          ' num2str((OmegaX\EX)'/gama,'%12.4f')]));       
disp(' ');