CERTAIN EQUIVALENCE FUNCTIONS

DEFINITION

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):

CEt =$-VALUE(t , par₁, par₂, ... , par_m)

= U^-1(E[U(x)]) = -t ln( E[EXP(-x/t )])

APPLICATION

If Math Model maps decision variables to payoff distribution parameters

M: (d₁, d₂, ... , d_n) --> (par₁, par₂, ... , par_m)

and CEt maps payoff distribution parameters to $-Value, can formulate decision problem as follows:

CHOOSE decision variables (d₁, d₂, ... , d_n) in such a way as to

MAXIMIZE CEt

Thus the CE-Value function becomes the objective function in a nonlinear programming problem.