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


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2008-12

AUTHORS

R. Elie

ABSTRACT

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. More... »

PAGES

411-431

References to SciGraph publications

Journal

TITLE

Applied Mathematics & Optimization

ISSUE

3

VOLUME

58

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00245-008-9044-y

DOI

http://dx.doi.org/10.1007/s00245-008-9044-y

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1040643981


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