Optimal Hedging in Incomplete Markets

George Bouzianis and Lane P. Hughston

Applied Mathematical Finance, 2020, vol. 27, issue 4, 265-287

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.

Date: 2020
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DOI: 10.1080/1350486X.2020.1819831

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