Finite Time Merton Strategy under Drawdown Constraint: A Viscosity Solution Approach

Finite Time Merton Strategy under Drawdown Constraint: A Viscosity Solution Approach 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, ( 2006 )) 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. Applied Mathematics and Optimization Springer Journals

Finite Time Merton Strategy under Drawdown Constraint: A Viscosity Solution Approach

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Copyright © 2008 by Springer Science+Business Media, LLC
Mathematics; Numerical and Computational Methods ; Mathematical Methods in Physics; Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
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