CE FUNCTION DEFINITION AND APPLICATION

DEFINITION

 A CE-VALUE FUNCTION is a mapping from the parameters of a probability distribution for monetary payoff and a risk tolerance value to a certain equivalent dollar value (via the exponential utility function):

 APPLICATION

 If a Mathematical Model maps decision variables (d₁, d₂, ..., d_n) to payoff distribution parameters (par₁, par₂, ... , par_m):

 and the CE-value function maps the payoff distribution parameters to a $-value, then we can formulate the decision problem as follows:

Thus the CE-value function becomes the objective function or maximand for the optimization problem. This reduces the problem of decision making under uncertainty into an ordinary nonlinear programming problem, for which a variety of algorithms exist based on the Kuhn-Tucker optimality conditions. Evaluating the partial derivatives appearing in the statement of these optimality conditions constitutes one of the main applications of the differential calculus to the Decision Science/Management Science arena.

 See: Method for deriving CE-value functions.