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.
- OSTI ID:
- 21241923
- Journal Information:
- Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 3 Vol. 58; ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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