Consumption processes and positively homogeneous projection properties
- 68 Downloads
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.
KeywordsConsumption strategies Income drawdown log-Lévy processes Martingale consumption Positive homogeneity Smooth bonus
JEL ClassificationE21 G22 G23
Mathematics Subject Classification (2000)91B28 93E99
Unable to display preview. Download preview PDF.