CAPITAL BUDGETING PROBLEM

Capital budgeting problem - In its elementary form, there is a fixed amount of capital, say C, that can be allocated to any of n investments. Each investment has a minimum level, say L, and a maximum level, say U. The expected return on investment is a function, v_j(x_j), where x_j is the level of the j-th investment opportunity (L_j <= x_j <= U_j). Risk is measured by a standard deviation from the expected return, say s_j(x_j). The problem is to maximize total expected return, subject to a budget constraint: Sum_j(x_j) <= C, and a risk constraint: Sum_j(v_j(x_j) + a_j s_j(x_j)) <= b, where a_j and b are parameters. The returns on the investments could be correlated. Then, if Q is the variance-covariance matrix, the risk constraint is quadratic: vx + x'Qx <= b. (Also see the portfolio selection problem .)