Department of Finance
Date of this Version
2005
Document Type
Article
Citation
Journal of Actuarial Practice 12 (2005), pp. 159-180
Abstract
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 through the control of the valuation rate (which is determined incorporating a certain feedback mechanism of the past contribution rate). The optimal solution for the deterministic case is obtained using standard calculus and the method of Lagrange multipliers.
Included in
Accounting Commons, Business Administration, Management, and Operations Commons, Corporate Finance Commons, Finance and Financial Management Commons, Insurance Commons, Management Sciences and Quantitative Methods Commons
Comments
Copyright 2005 Absalom Press