Dynamic Utility Optimization

Model Portfolio
import S "Stock price"
import EUR "Numeraire"
import Port_0 "Initial portfolio value"
import T "Investment horizon"
import n_dt "Number of rebalances"
export Port_obs "Portfolio"
export d_obs "Optimal ratio"
 
	% initialize C with values from [0...1]
	index = 0
	n = 10
	loop n+1 
		C[index+1] = index/n
		index = index + 1		
	end
 
	Port = Port_0		
	Port_obs = Port
	loop n_dt		
		% optimization by brute force,
		% implements d = argmax_{d}(E(utility(Port!)))
		util = -1E10
 
		loop c, pi, cur_util:C, Pi, Util
			% compute utility calling a userdefined Matlab function
			cur_util = E(utility(return!))
			return = pi!/Port_0
			% remember portfolio weight d with largst utility 
			if cur_util> util
				d = c
				util = cur_util
			end		 				
		end 
		u = Util
 
		% Compute all possible outcomes of the portfolio
		% for optimization  
		loop pi, c : Pi, C
			pi = Port + c*(S!-S) + (1-c)*(100/EUR!-100/EUR)
		end		
		% Investment in S or Zero Bond (with value 1/EUR)
		Port = Port + d*(S!-S) + (1-d)*(100/EUR!-100/EUR)						
		d_obs = d
 
		Theta T/n_dt
 
		Port_obs = Port																																
	end
end