gamblersfortune.java

金融资产定价,随机过程,MONTE CARLO 模拟 JAVA 程序和文档资料

/* WARANTY NOTICE AND COPYRIGHT
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.

Copyright (C) Michael J. Meyer

[e-mail]
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*/




/*
 * GamblersFortune.java
 *
 * Created on January 18, 2002, 5PM
 */
 
package Examples.Probability;

import Statistics.*;
import Processes.*;
import java.lang.Math.*;


 

/** <p>Console program setting up a biased random walk X and checking the 
 * gambler's expected winnings (losses really) and the probability of losing it
 * all under the following stopping rule:</p>
 *
 *<p>Stop after 20000 throws or if you are 5 ahead or 100 down, whichever 
 *comes first.</p>
 *
 * @author  Michael J. Meyer
 */
public class GamblersFortune{

   
    public static void main(String[] args)
    {
          
        String message;
        message="Starting with zero dollars we bet repeatedly one dollar\n"+
                "on the throw of a coin where the odds are 0.499/0.501\n"+
                "against us. We examine expected winnings under a\n"+
                "stopping strategy.\n\n";
        System.out.println(message);
                        
        
        int T=20000;     //time steps to horizon
        double X_0=0.0;   //initial value
        
        final BiasedRandomWalk X=new BiasedRandomWalk(T,X_0,0.499);
        
        message="Strategy: we stop after 20000 throws or if we are\n"+
                "5 ahead or 100 down, whichever comes first.\n"+
                "Expectations computed from 50000 paths. "+
                "Patience, it takes a while.\n";
        System.out.println(message);

 
        //here's the quitting rule, an abstract class instantiated
        //in front of your very eyes:
        StoppingTime tau=new StoppingTime(){
        
             public boolean stop(int t)
             {
                 final double[] path=X.get_path();
                 return ((t==20000)||(path[t]==+5)||(path[t]==-100));  }
                 
        }; //end tau
        
        //the random walk sampled at tau
        final RandomVariable X_tau=X.sampledAt(tau);
        
        //Monte Carlo mean, sample size 50000
        double E=X_tau.expectation(50000);
        //cut this down to 5 decimals
        E=1.0*Math.round(10000*E)/10000;
        
        message="Expected winnings = "+E;
        System.out.println(message);
        
        //indicator function of the event [X_tau=-1000]
        RandomVariable Y=new RandomVariable(){
         
            public double getValue(int t)
            {
                return (X_tau.getValue(t)==-100) ? 1:0;  }
                
        }; //end Y
        
        // probability of total loss
        double q=Y.expectation(50000);
        //cut this down to 5 decimals
        q=1.0*Math.round(10000*q)/10000;
        
        message="Probability of losing 100 = "+q;
        System.out.println(message);
        
        
   } //end main
   
   
   
}//end Gambler's fortune