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An Application Of Control Theory To The Individual Aggregate Cost Method, Alexandros A. Zimbidis, Steven Haberman
An Application Of Control Theory To The Individual Aggregate Cost Method, Alexandros A. Zimbidis, Steven Haberman
Journal of Actuarial Practice (1993-2006)
The paper investigates the individual aggregate cost method (also known as the individual spread-gain method), which is normally applicable in small pension funds or fully contributory schemes, using a control theoretical framework. We construct the difference equations describing the mechanisms of the respective funding method and then calculate the optimal control path of the contribution rate assuming (first) a stochastic and (second) a deterministic pattern for the future investment rates of return. For the first case, the optimal solution is achieved through a linear approximation and using stochastic optimization techniques. It is proved that the contribution rate is (optimally) controlled …