function z = maxgleichungrisky(X)

%y0 ->the optimal initial value-to.debt ratio after recapitalization
%l -> lower bound of y
%u -> uper bound of y
%B -> face value of firm's debt
%I -> instantaneous coupon rate
%nydach -> risk-adjusted expected rate of return on the firm's unlevered assets
%X=[y0,l,u,B,I,nydach]

% Optimierung läuft über maxgglechung
% Problem : maximiere V(y0,B,l,u)-kB über y0,l,u,B,I und nydach
% unter den Nebenbedingungen:
% 1)V(0,B,l,u)=B(y0+k) <=> V(y0,B,l,u)-k*B=B*y0
% 2)E(y=l,B,l,u)>=0
% 3)D(y0,B,l,u)=B <=> B*y0=D(y0,B,l,u)*y0

% Problem umgeformt : maximmiere D(y0,B,l,u)*y0
% unter der Nebenbedingung:
% E(y=l,B,l,u)>=0

% oder :minimiere k*B-D(y0,B,l,u)*y0
% unter der Nebenbedingung:
% E(y=l,B,l,u)=<0

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Parameter
g=0.2;
sigma=0.03;
tetap=0.5;
r=0.3;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
df=max(X(2)-g, 0);
a=0.5 - X(6)/(sigma^2);
b=sqrt(a^2 + 2*r*(1-tetap)/(sigma^2));
m1=a+b;
m2=a-b;
Delta=X(3)^m1*X(2)^m2-X(3)^m2*X(2)^m1;

    
D1=(X(4)/Delta)*((1-X(5)/r)*X(2)^m2-(df-X(5)/r)*X(3)^m2);
D2=(X(4)/Delta)*((df-X(5)/r)*X(3)^m1-(1-X(5)/r)*X(2)^m1);
    
D=D1*X(1)^m1+D2*X(1)^m2+X(5)/r*X(4);  %Debt Value for risky debt
    

z=0-D*X(1); %Minimierungsgleichung