Finance and Stochastics

, Volume 12, Issue 3, pp 357–380 | Cite as

Consumption processes and positively homogeneous projection properties

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Abstract

We constructively prove the existence of time-discrete consumption processes for stochastic money accounts that fulfill a pre-specified positively homogeneous projection property (PHPP) and let the account always be positive and exactly zero at the end. One possible example is consumption rates forming a martingale under the above restrictions. For finite spaces, it is shown that any strictly positive consumption strategy with restrictions as above possesses at least one corresponding PHPP and could be constructed from it. We also consider numeric examples under time-discrete and -continuous account processes, cases with infinite time horizons, and applications to income drawdown and bonus theory.

Keywords

Consumption strategies Income drawdown log-Lévy processes Martingale consumption Positive homogeneity Smooth bonus 

JEL Classification

E21 G22 G23 

Mathematics Subject Classification (2000)

91B28 93E99 

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References

  1. 1.
    Cox, J.C., Huang, C.F.: Optimal consumption and portfolio policies when asset prices follow a diffusion process. J. Econ. Theory 49, 33–83 (1989) MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Karatzas, I., Lehoczky, J.P., Shreve, S.E.: Optimal portfolio and consumption decisions for a “small investor” on a finite horizon. SIAM J. Control Optim. 27, 1157–1186 (1987) MathSciNetGoogle Scholar
  3. 3.
    Merton, R.C.: Optimum consumption and portfolio rules in a continuous time model. J. Econ. Theory 3, 373–413 (1971) CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Maxwell Institute for Mathematical Sciences, and Actuarial Mathematics and StatisticsHeriot-Watt UniversityEdinburghUK

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