Utility maximization with ratchet and drawdown constraints on consumption in incomplete semimartingale markets. (English) Zbl 1530.91556
Summary: In this paper, we study expected utility maximization under ratchet and drawdown constraints on consumption in a general incomplete semimartingale market using duality methods. The optimization is considered with respect to two parameters: the initial wealth and the essential lower bound on consumption process. In order to state the problem and define the primal domains, we introduce a natural extension of the notion of running maximum to arbitrary nonnegative optional processes and study its properties. The dual domains for optimization are characterized in terms of solidity with respect to an ordering that is introduced on the set of nonnegative optional processes. The abstract duality result we obtain for the optimization problem is used in order to derive a more detailed characterization of solutions in the complete market case.
MSC:
| 91G15 | Financial markets |
| 93E20 | Optimal stochastic control |
| 91G80 | Financial applications of other theories |
| 91B16 | Utility theory |
Keywords:
utility maximization; convex duality; ratcheting of consumption; drawdown constraint on consumption; running maximum; incomplete marketsReferences:
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