Joint investment strategies with a superadditive capitalization function

Some financial investments offer different profitabilities according to the invested amounts. They are operations which differentiate rates of interest depending on the placed capital, i.e., operations whose underlying capitalization functions are not linear with respect to the invested sums. Usually, this differentiation is performed by assigning a variable rate that is an increasing function of the amounts at given jump points, and constant in each interval. As a result, the capitalization function is discontinuous with a finite number of jumps, once the investment term has been fixed. In this situation, an investor can take advantage of differentials in interest rates between two intervals and so it could be convenient, for a group of investors, to join their quantities of money because greater rates of interest can be achieved. The question is how to fairly distribute, among the individual agents, the obtained joint interest. Our answer is based on a modified snaring, according to the interests generated by a new continuous capitalization function which "covers" the discontinuities of the original function.