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Optimal Hedging in Incomplete Markets

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  • George Bouzianis
  • Lane P. Hughston

Abstract

We consider the problem of optimal hedging in an incomplete market with an established pricing kernel. In such a market, prices are uniquely determined, but perfect hedges are usually not available. We work in the rather general setting of a Lévy-Ito market, where assets are driven jointly by an n-dimensional Brownian motion and an independent Poisson random measure on an n-dimensional state space. Given a position in need of hedging and the instruments available as hedges, we demonstrate the existence of an optimal hedge portfolio, where optimality is defined by use of a least expected squared error criterion over a specified time frame, and where the numeraire with respect to which the hedge is optimized is taken to be the benchmark process associated with the designated pricing kernel.

Suggested Citation

  • George Bouzianis & Lane P. Hughston, 2020. "Optimal Hedging in Incomplete Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(4), pages 265-287, July.
    • Handle: RePEc:taf:apmtfi:v:27:y:2020:i:4:p:265-287
    DOI: 10.1080/1350486X.2020.1819831
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