Portfolio Optimization under Shortfall Risk Constraint

Oliver Janke and Qinghua Li

Papers from arXiv.org

Abstract: This paper solves a utility maximization problem under utility-based shortfall risk constraint, by proposing an approach using Lagrange multiplier and convex duality. Under mild conditions on the asymptotic elasticity of the utility function and the loss function, we find an optimal wealth process for the constrained problem and characterize the bi-dual relation between the respective value functions of the constrained problem and its dual. This approach applies to both complete and incomplete markets. Moreover, the extension to more complicated cases is illustrated by solving the problem with a consumption process added. Finally, we give an example of utility and loss functions in the Black-Scholes market where the solutions have explicit forms.

Date: 2015-01, Revised 2016-04
New Economics Papers: this item is included in nep-rmg and nep-upt
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Published in Optimization, 65(9), 1733-1755 (2016)

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