Some Notes on the Dynamics and Optimal Control of Stochastic Pension Fund Models in Continuous Time

Andrew Cairns

ASTIN Bulletin, 2000, vol. 30, issue 1, 19-55

Abstract: This paper discusses the modelling and control of pension funds. A continuous-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 modern portfolio theory. A general quadratic loss function is proposed which provides an explicit 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 schemes 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. Power and exponential loss functions are then investigated and related problems discussed. 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.

Date: 2000
References: Add references at CitEc
Citations: View citations in EconPapers (62)

Downloads: (external link)
https://www.cambridge.org/core/product/identifier/ ... type/journal_article link to article abstract page (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cup:astinb:v:30:y:2000:i:01:p:19-55_00

Access Statistics for this article

More articles in ASTIN Bulletin from Cambridge University Press Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK.
Bibliographic data for series maintained by Kirk Stebbing ().