Surplus management under a stochastic process

Abstract

To immunize an insurance company's surplus against interest-rate fluctuations, asset-liability managers commonly adopt the so-called classical immunization strategy to set the duration of the surplus equal to zero. Unfortunately, this strategy is derived on the basis of the flat-term structure. This article examines the immunization strategy with a stochastic process, which can generate a mean-reverting term structure. By means of the stochastic process, the authors provide a measurement for evaluating the assets and liabilities of the insurance company. The authors also show that the immunization strategy suggested in the article is a general model and includes the classical immunization strategy as a special case. Furthermore, if a firm's objective is to maximize its convexity of the surplus subject to zero surplus duration and its budget constraint, the authors demonstrate that linear programming can implement the optimal immunization strategy in this case. Moreover, the results of this simulation show that the cost of failing to recognize stochastic interest-rate changes can be extremely high.