gamblersfortune_1.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_1.java
 *
 * Created on January 23, 2002, 6:20 PM
 */
 
 
package Examples.Probability;

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


 

/** <p> Gambler starts with 6 dollars and bets 1 dollar on unfavorably loaded
 * coin (0.49/0.51) until he has 10 dollars or is wiped out. Random walk
 * allocated as a Markov chain. Possible states of the fortune 0,1,2,...,10.
 * Computes terminal (equilibrium) probability distribution.</p>
 *
 * @author  Michael J. Meyer
 */
public class GamblersFortune_1{


    public static void main(String[] args)
    {
    
         final int T=2000;        //time steps to horizon
         double j_0=6;            //initial fortune
        
         final double p=0.49;  //probability of success
         
         String message=
          "Gambler starts with 6 dollars and bets 1 dollar on unfavorably\n"+ 
          "loaded coin (0.49/0.51) until he has 10 dollars or is wiped out.\n"+ 
          "Possible states of the fortune 0,1,2,...,10.\n\n"+
          "Probabilities of being in state j=0,1,...,10 at time T= "+T+
          ":\nPatience it takes a while:\n";
          System.out.println(message);
 
    
         /* allocate gamblers fortune as a Markov chain on the fly by defining 
          * the transition probabilities q(t,i,j) in the body of the 
          * constructor call
          */
         final MarkovChain gf=new MarkovChain(T,j_0){
    
             public double q(int t, int i, int j)
             {
                 if((i==0)&&(j==0)) return 1;
                 if ((i==10)&&(j==10)) return 1;
                 if((i>0)&&(i<10))
                 {
                     if(j==i-1) return 1-p;
                     if(j==i+1) return p;     }
                
                 return 0;    // all other cases

              } //end q
         
          };// end gf
     
          //allocate the ramdom vector  X=(1_{[gf_T=j]})_{j=0,...,10}
          RandomVector X=new RandomVector(11){
     
               public double[] getValue(int t)
               {
                   double[] x=new double[11];
                   double[] path=gf.get_path();
                   gf.newPathBranch(t);
                   x[(int)path[T]]=1;    //all other components zero
                   return x;
                } //end getValue
          
          }; // end X
     
     
          //expectation of X over 10000 paths
          double[] Q=X.expectation(10000);
     
          for(int i=0;i<11;i++)
          {
              Q[i]=1.0*Math.round(1000*Q[i])/1000;
              System.out.print(Q[i]+" ");
           }
           
      } // end main
      
 } // end GamblersFortune_1