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- ClearAll[Y ,X,z,w];
- T0=1 ;
- Hmu=0.0;
- SA=10+Hmu ;
- SB=10-Hmu;
- Sigma=1.5;
- K=10;
- r=1.02;
- gamma=0.1;
- Vi=2;
- Eye=2;
- ZC=(K-SA)/Sigma;
- ZB=(K-SB)/Sigma ;
- S0=(SA-gamma(Sigma^2)(Vi /Eye ))/r
- 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
- yy=1;
- ww=1;
- xx=0;
- yy=0;
- While[xx +zz <>2 && yy+ww<>0
- A==(((Vi /Eye ) -X)S0-Y*C0)r+X*SA-(gamma/2)(X^2)(Sigma^2)
- B==(((Vi /Eye ) -X)S0-Y*C0)r +(X +Y)SA -(gamma/2)((X +Y) ^2)(Sigma^2) -Y *K
- Q==(((Vi /Eye ) -z)S0-w*C0)r+z*SB-(gamma/2)(z^2)(Sigma^2)
- P==(((Vi /Eye ) -z)S0-w*C0)r +(z +w)SB -(gamma/2)(z +w) ^2(Sigma^2) -w *K
- 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 ])
- 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 ])
- AMAX==Maximize[UA ,{X >=0,X<=2,Y>=-1,Y<=1},{X ,Y}]
- BMAX==Maximize[UB ,{z >=0,z<=2,w>=-1,w<=1},{z ,w}]
- xx==Replace[X,AMAX [[2,1]]]
- yy==Replace[Y,AMAX [[2,2]]]
- zz==Replace[z,BMAX [[2,1]]]
- ww==Replace[w,BMAX [[2,2]]]
- If[xx +zz<2.00005,S0=S0-0.000001,If[xx+zz>2.00005,S0,S0+0.000001,S0]]
- If[yy +ww<0.00005,C0=C0-0.000001,If[yy+ww>0.00005,C0,C0+0.000001,C0]]
- ]
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