Finite Time Merton Strategy under Drawdown Constraint: A Viscosity Solution Approach
Elie, Romuald (2008), Finite Time Merton Strategy under Drawdown Constraint: A Viscosity Solution Approach, Applied Mathematics and Optimization, 58, 3, p. 411-431. http://dx.doi.org/10.1007/s00245-008-9044-y
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00362305/en/
Journal nameApplied Mathematics and Optimization
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Abstract (EN)We consider the optimal consumption-investment problem under the drawdown constraint, i.e. the wealth process never falls below a fixed fraction of its running maximum. We assume that the risky asset is driven by the constant coefficients Black and Scholes model and we consider a general class of utility functions. On an infinite time horizon, Elie and Touzi (Preprint, ) provided the value function as well as the optimal consumption and investment strategy in explicit form. In a more realistic setting, we consider here an agent optimizing its consumption-investment strategy on a finite time horizon. The value function interprets as the unique discontinuous viscosity solution of its corresponding Hamilton-Jacobi-Bellman equation. This leads to a numerical approximation of the value function and allows for a comparison with the explicit solution in infinite horizon.
Subjects / KeywordsConsumption-investment strategy - Drawdown constraint - Viscosity solution - Comparison principle
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