Beberapa catatan pada model dana pensiun stokastik dengan waktu kontinu pada kasus fungsi objektif berbentuk kuadratis

Abstract

This paper discusses the modelling and control of pension funds. A contino us-time stochastic pension fund model is proposed in which there are n risky assets plus the risk-free asset as well as randomness in the level of benefit outgo. We consider Markov control strategies which optimise over the contribution rate and over the range of possible asset-allocation strategies. For a general (not necessarily quadratic) loss function it is shown that the optimal proportions of the fund invested in each of the risky assets remain constant relative to one another. Furthermore, the asset allocation strategy always lies on the capital market line familiar from modem portfolio theory. A general quadratic loss function is proposed which provides an axplicit solution for the optimal contribution and asset-allocation strategies. It is noted that these solutions are not dependent on the level of uncertainty in the level of benefit outgo, suggesting that small schcmes should operate in the same way as large ones. The optimal asset-allocation strategy, however, is found to be counterintuitive leading to some discussion of the form of the loss function. The stationary distribution of the process is considered and optimal strategies compared with dynamic control strategies. Finally there is some discussion of the effects of constraints on contribution and asset allocation strategies.