Three-Currency Deposit Diversification: Savage’s Principle Approach

Abstract

The problem of optimal multi-currency deposit diversification with uncertain future exchange rates is studied as the problem of the minimization of the lost profit. It is assumed that only the ranges of these uncertain parameters are known. The Savage minimax regret conception is used to minimize the lost profit (risk by Savage) caused by uncertainty. The risk function and the function of the guaranteed risk are calculated in an explicit form. After that, the problem is reduced to finding the point of the minimum of a piecewise linear function under simple linear constraints. Explicit formulas for nine ”representative” point-candidates for the optimal solution are found. The final choice is made by direct comparison of the values of the Savage criterion at these points.