Coherent hedging in incomplete markets

Birgit Rudloff

Quantitative Finance, 2009, vol. 9, issue 2, 197-206

Abstract: In incomplete financial markets, not every contingent claim can be perfectly replicated by a self-financing strategy. In this paper, we minimize the risk that the value of the hedging portfolio falls below the payoff of the claim at time T. We use a coherent risk measure, introduced by Artzner et al., to measure the risk of the shortfall. The dynamic optimization problem of finding a self-financing strategy that minimizes the coherent risk of the shortfall can be split into a static optimization problem and a representation problem. We will deduce necessary and sufficient optimality conditions for the static problem using convex duality methods. The solution of the static optimization problem turns out to be a randomized test with a typical 0-1 structure. Our results improve those obtained by Nakano. The optimal hedging strategy consists of superhedging a modified claim that is the product of the original payoff and the solution to the static problem.

Keywords: Hedging; Shortfall risk; Coherent risk measures; Convex duality; Generalized Neyman-Pearson lemma (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://www.tandfonline.com/doi/abs/10.1080/14697680802169787 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:quantf:v:9:y:2009:i:2:p:197-206

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/RQUF20

DOI: 10.1080/14697680802169787

Access Statistics for this article

Quantitative Finance is currently edited by Michael Dempster and Jim Gatheral

More articles in Quantitative Finance from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().