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Neofytos Rodosthenous () and Mihail Zervos ()
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Neofytos Rodosthenous: Queen Mary University of London
Mihail Zervos: London School of Economics

Finance and Stochastics, 2017, vol. 21, issue 1, No 4, 157-186

Abstract: Abstract We consider a new family of derivatives whose payoffs become strictly positive when the price of their underlying asset falls relative to its historical maximum. We derive the solution to the discretionary stopping problems arising in the context of pricing their perpetual American versions by means of an explicit construction of their value functions. In particular, we fully characterise the free-boundary functions that provide the optimal stopping times of these genuinely two-dimensional problems as the unique solutions to highly nonlinear first order ODEs that have the characteristics of a separatrix. The asymptotic growth of these free-boundary functions can take qualitatively different forms depending on parameter values, which is an interesting new feature.

Keywords: Optimal stopping; Running maximum process; Variational inequality; Two-dimensional free-boundary problem; Separatrix; 49L20; 60G40 (search for similar items in EconPapers)
JEL-codes: C61 G13 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s00780-016-0319-x

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