Drawing solutions

Hi

For a couple of months I have been struggling with the same problem. The problem is that I would like to draw the following restrictions:

D(2.7,1,1,0.3)=D(c,delta,xT,0.2)
S(2.7,1,1,0.3)<S(c,delta,xT,0.2)

where S is found with the following

function S0 = S0Func(obj, c, delta, xT, sigma)
          beta = obj.betaFunc(sigma);
          xb = obj.xbFunc(c, delta, sigma);            
          S0 = (1-obj.tau).*(obj.x0./(obj.r-obj.mu)-c./obj.r-(xb./(obj.r-obj.mu)-c./obj.r).*((obj.x0./xb).^beta)-((delta-1).*c./obj.r).*((obj.x0./xT).^beta-((obj.x0./xb).^beta)));
end

and D is found with the follwing

function D0 = D0Func(obj, c, delta, xT, sigma)            
          beta = obj.betaFunc(sigma);
          xb = obj.xbFunc(c, delta, sigma);            
          L = obj.LFunc(xb);            
          D0 = c./obj.r+(L-c./obj.r).*((obj.x0./xb).^beta)+((delta-1).*c./obj.r).*((obj.x0./xT).^beta-((obj.x0./xb).^beta));
end

Please write if you would like the complete code.

Furthermore I have some restrictions which has to be fulfilled.

• delta > 1
• c > 0
• 1>xT>xb

I can draw the functions without the restrictions using

[xT, delta, c] = meshgrid(0.8:.01:1, 1:.1:3, 0:.1:4);
values = calc.S0Func(optimalStraightCoupon,1, 1, calc.sigmaH)- calc.S0Func(c,delta, xT, calc.sigmaL);            
patch(isosurface(-xT, -c, -delta, values, 1), 'FaceColor', 'red');
view(3);

What I would like to do is draw the values of c, delta, xT, which solve this problem and in the same time maximizes the S function.

I am a bit frustrated as I have been spending a lot of time on the project and I need to get this right.

Any help is very appreciated.