The Merton Problem with a Drawdown Constraint on Consumption
AbstractIn this paper, we work in the framework of the Merton problem but we impose a drawdown constraint on the consumption process. This means that consumption can never fall below a fixed proportion of the running maximum of past consumption. In terms of economic motivation, this constraint represents a type of habit formation where the investor is reluctant to let his standard of living fall too far from the maximum standard achieved to date. We use techniques from stochastic optimal control and duality theory to obtain our candidate value function and optimal controls, which are then verified.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1210.5205.
Date of creation: Oct 2012
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-10-27 (All new papers)
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