Maximization symbolic function with piecewise symbolic functions

Hello,

i have the following code:

syms R K L ext_mon


T = 100;

%Company
gamma = 0.03;
A_0 = 100;
debt = 0;
ext_cost = symfun(ext_mon*1.03^T,ext_mon);

%Insurer
AI_0 = 200;
LI_0 = 100;
mu_L = 0.02;
mu_A = 0.03;
sigma_L = 0.002;
sigma_A = 0.001;

prem = symfun(R+K,[R K]);
A_T = symfun((1+gamma)*(A_0+prem),[R K]);

expAI = symfun((AI_0 + prem(R,K))* exp((mu_A + (sigma_A^2/2))*T),[R K]);
expLI_tilde= LI_0*exp((mu_L + (sigma_L^2/2))*T); 

X= symfun(piecewise(L<R,L,R<=L<=K,R,L>K,R+L-K),[R K]);
Y= symfun(piecewise(L<R,0,R<=L<=K,L-R,L>K,K-R),[R K]);
D = symfun(piecewise((Y(R,K) - expAI(R,K) - expLI_tilde)>0,Y(R,K) - expAI(R,K) - expLI_tilde,0),[R K]);


S_T = symfun(A_T - debt - L - X - D,[R K]);
Investment = symfun(S_T(R,K) + ext_mon,[R K]);
GrossReturn = symfun(Investment(R,K)*1.03^T,[R K]);

Profit = symfun(GrossReturn(R,K) - Investment(R,K) - ext_cost(ext_mon),[R K ext_mon]);

I want now to maximize "Profit" under R,K and ext_mon.

When i use fminsearch(-Profit,[0 1 0]), i get the error

fminsearch(-Profit,[0 1 0])

Error using symfun/subsref (line 189)
Invalid argument at position 2. Symbolic function expected 3 input arguments but received 1.

Error in fminsearch (line 201)
fv(:,1) = funfcn(x,varargin{:});

Error using symfun/subsref

Invalid argument at position 2. Symbolic function expected 3 input arguments but received 1.

Error in fminsearch (line 200)

I tried already to convert the symbolic function with matlabFunction, but there i get the error

Unable to generate code for piecewise for use in anonymous functions.

Can someone help me, how i can maximize the symbolic function ?

Best

Answer 1

[Walter Roberson]

syms R K L ext_mon
T = 100;
%Company
gamma = 0.03;
A_0 = 100;
debt = 0;
ext_cost = symfun(ext_mon*1.03^T,ext_mon);
%Insurer
AI_0 = 200;
LI_0 = 100;
mu_L = 0.02;
mu_A = 0.03;
sigma_L = 0.002;
sigma_A = 0.001;
prem = symfun(R+K,[R K]);
A_T = symfun((1+gamma)*(A_0+prem),[R K]);
expAI = symfun((AI_0 + prem(R,K))* exp((mu_A + (sigma_A^2/2))*T),[R K]);
expLI_tilde= LI_0*exp((mu_L + (sigma_L^2/2))*T); 
X= symfun(piecewise(L<R,L,R<=L<=K,R,L>K,R+L-K),[R K]);
Y= symfun(piecewise(L<R,0,R<=L<=K,L-R,L>K,K-R),[R K]);
D = symfun(piecewise((Y(R,K) - expAI(R,K) - expLI_tilde)>0,Y(R,K) - expAI(R,K) - expLI_tilde,0),[R K]);
S_T = symfun(A_T - debt - L - X - D,[R K]);
Investment = symfun(S_T(R,K) + ext_mon,[R K]);
GrossReturn = symfun(Investment(R,K)*1.03^T,[R K]);
Profit = symfun(GrossReturn(R,K) - Investment(R,K) - ext_cost(ext_mon),[R K ext_mon]);

Profit

Profit(R, K, ext_mon) = 

negProfit = -Profit

negProfit(R, K, ext_mon) = 

tn = tempname + ".m";

negProfitfun = matlabFunction(negProfit, 'vars', {[R, K, ext_mon, L]}, 'File', tn, 'optimize', false)

negProfitfun = function_handle with value:
    @tpa9357521_4971_4509_a300_405e8eb79603

ph = fileparts(tn);
addpath(ph)
opts = optimset(@fminsearch);
opts.MaxFunEvals = 1e5;
opts.MaxIter = 1e5;
[bestvars, negprofit] = fminsearch(negProfitfun, [0 1 0 0], opts);

 
Exiting: Maximum number of function evaluations has been exceeded
         - increase MaxFunEvals option.
         Current function value: -Inf 

profit = -negprofit;

fprintf('Profit %g at R = %g, K = %g, ext_mon = %g, L = %g\n', profit, bestvars);

Profit Inf at R = 9.89433e+303, K = 1.04843e+307, ext_mon = 8.42195e+303, L = -3.44808e+304