MULTI-STAGE OPTIMIZATION FOR LONG-TERM INVESTORS

John M. Mulvey
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John M. Mulvey: Department of Operations Research and Financial Engineering, Bendheim Center for Finance, Princeton University, Princeton, NJ 08544, USA

Chapter 3 in Quantitative Analysis in Financial Markets:Collected Papers of the New York University Mathematical Finance Seminar(Volume III), 2002, pp 66-85 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractMulti-stage simulation and optimization models are effective for solving long-term financial planning problems. Prominent examples include: asset-liability management for pension plans, integrated risk management for insurance companies, and long-term planning for individuals. Several applications will be briefly mentioned.A multi-stage framework provides advantages over single-period myopic approaches. First, the investor gains an understanding of the risks that a long-term goal will be unfulfilled, such as retiring with adequate wealth. A multi-stage model can be more realistic than a single period model. Thus, assets such as equity, which reduce long-term risks while increasing short-term volatility, can be evaluated in a temporal setting. The tradeoff between long- and short-term gains becomes apparent in a multi-period context. As a second advantage, enhanced returns are possible with dynamic investment strategies. For instance, the traditional approach of rebalancing assets to a fixed strategic benchmark generates higher returns when assets possess increased volatility. This “volatility pumping” is dampened by transaction and market impact costs. Only by solving a multi-stage optimization model can we discover the optimal rebalancing rules. Likewise, moving a large portfolio to a new strategic benchmark can be optimized. As a third example, individuals often hold assets with large embedded gains. Selling these assets triggers a capital gains tax. Again, these decisions can be evaluated by means of a multi-stage model. A real-world example from pension planning illustrates the concepts.Three distinct approaches are available for solving the multi-stage optimization model: (1) dynamic stochastic control, (2) stochastic programming, and (3) optimizing a stochastic simulation model. We briefly review the pros and cons of these approaches; it seems unlikely that a single approach will dominate the others. We conclude with some topics for future research.

Keywords: Quantitative Analysis; Financial Markets (search for similar items in EconPapers)
Date: 2002
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