Shortfall risk through Fenchel duality

Zhenyu Cui and Jun Deng ()
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Zhenyu Cui: School of Business, Stevens Institute of Technology, Hoboken, USA
Jun Deng: School of Banking and Finance, University of International Business and Economics, Beijing, P. R. China

International Journal of Financial Engineering (IJFE), 2018, vol. 05, issue 02, 1-14

Abstract: In this paper, we propose a Fenchel duality approach to study the minimization problem of the shortfall risk. We consider a general increasing and strictly convex loss function, which may be more general than the situation of convex risk measures usually assumed in the literature. We first translate the associated stochastic optimization problem to an equivalent static optimization problem, and then obtain the explicit structure of the optimal randomized test for both complete and incomplete markets. For the incomplete market case, to the best of our knowledge, we obtain for the first time the explicit randomized test, while previous literature only established the existence through the supermartingale optional decomposition approach. We also solve the shortfall risk minimization problem for an insider through the enlargement of filtrations approach.

Keywords: Shortfall risk; Fenchel duality; enlargement of filtration; risk measure; hedging (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S2424786318500196

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