Elasticity Approach to Portfolio Optimization
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Portfolio optimization has been one of the most heavily researched areas in finance dating back to the work by Markowitz (1952) who used a discrete one period model to develop his theory. Merton (1969, 1971) was the first to solve portfolio problems in a continuous-time setting by applying stochastic control techniques. Using ideas presented in the seminal papers by Harrison/Kreps (1979) and Harrison/Pliska (1981, 1983), an alternative approach — the socalled martingale approach — was developed by Pliska (1986), Cox/Huang (1989, 1991), and Karatzas/Lehoczky/Shreve (1987). In each of these papers the portfolio problems were formulated with respect to the investment opportunities of an investor. In this chapter it will be shown that an investor actually optimizes over elasticities and — in the case of stochastic interest rates — over durations. Using this elasticity approach to portfolio optimization(EAPO), one can apply a kind of two-step procedureto solve portfolio problems. Firstly, one determines the optimal elasticity, which in a complete market is independent of a specific asset. Secondly, a strategy is computed which tracks this elasticity. Our method proves to be especially useful when portfolio problems with contingent claims are studied. It allows to focus on so-called reduced portfolio problems.We wish to emphasize that our approach is applicable both to the stochastic control approach and the martingale approach. Nevertheless, using a two-step procedure can be interpreted as a parallel to the martingale approach.
KeywordsPortfolio Optimization Contingent Claim Bond Price Short Rate Investment Horizon
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