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May 21st, 2018
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  1. ClearAll[Y ,X,z,w];
  2. T0=1 ;
  3. Hmu=0.0;
  4. SA=10+Hmu ;
  5. SB=10-Hmu;
  6. Sigma=1.5;
  7. K=10;
  8. r=1.02;
  9. gamma=0.1;
  10. Vi=2;
  11. Eye=2;
  12.  
  13. ZC=(K-SA)/Sigma;
  14. ZB=(K-SB)/Sigma ;
  15. S0=(SA-gamma(Sigma^2)(Vi /Eye ))/r
  16. C0=((SA-gamma(Sigma^2)(Vi /Eye ) -K)(1-CDF[NormalDistribution[0, 1], ZC+gamma*Sigma*(Vi /Eye ) ])+(PDF[NormalDistribution[0, 1], ZC+gamma*Sigma*(Vi /Eye ) ])Sigma)/r
  17. yy=1;
  18. ww=1;
  19. xx=0;
  20. yy=0;
  21. While[xx +zz <>2 && yy+ww<>0
  22. A==(((Vi /Eye ) -X)S0-Y*C0)r+X*SA-(gamma/2)(X^2)(Sigma^2)
  23. B==(((Vi /Eye ) -X)S0-Y*C0)r +(X +Y)SA -(gamma/2)((X +Y) ^2)(Sigma^2) -Y *K
  24. Q==(((Vi /Eye ) -z)S0-w*C0)r+z*SB-(gamma/2)(z^2)(Sigma^2)
  25. P==(((Vi /Eye ) -z)S0-w*C0)r +(z +w)SB -(gamma/2)(z +w) ^2(Sigma^2) -w *K
  26. UA==-Exp[-gamma*A]*(CDF[NormalDistribution[0, 1], ZC+gamma*X *Sigma ]) -Exp[-gamma*B]*(1-CDF[NormalDistribution[0, 1], ZC+gamma*(X +Y )*Sigma ])
  27. UB==-Exp[-gamma*Q ]*(CDF[NormalDistribution[0, 1], ZB+gamma*z *Sigma ]) -Exp[-gamma*P ]*(1-CDF[NormalDistribution[0, 1], ZB+gamma*(z+w )*Sigma ])
  28. AMAX==Maximize[UA ,{X >=0,X<=2,Y>=-1,Y<=1},{X ,Y}]
  29. BMAX==Maximize[UB ,{z >=0,z<=2,w>=-1,w<=1},{z ,w}]
  30. xx==Replace[X,AMAX [[2,1]]]
  31. yy==Replace[Y,AMAX [[2,2]]]
  32. zz==Replace[z,BMAX [[2,1]]]
  33. ww==Replace[w,BMAX [[2,2]]]
  34. If[xx +zz<2.00005,S0=S0-0.000001,If[xx+zz>2.00005,S0,S0+0.000001,S0]]
  35. If[yy +ww<0.00005,C0=C0-0.000001,If[yy+ww>0.00005,C0,C0+0.000001,C0]]
  36. ]
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