March 2015 Stochastic monotonicity and duality of kth order with application to put-call symmetry of powered options
Vassili N. Kolokoltsov
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J. Appl. Probab. 52(1): 82-101 (March 2015). DOI: 10.1239/jap/1429282608

Abstract

We introduce a notion of kth order stochastic monotonicity and duality that allows us to unify the notion used in insurance mathematics (sometimes refereed to as Siegmund's duality) for the study of ruin probability and the duality responsible for the so-called put-call symmetries in option pricing. Our general kth order duality can be interpreted financially as put-call symmetry for powered options. The main objective of this paper is to develop an effective analytic approach to the analysis of duality that will lead to the full characterization of kth order duality of Markov processes in terms of their generators, which is new even for the well-studied case of put-call symmetries.

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Vassili N. Kolokoltsov. "Stochastic monotonicity and duality of kth order with application to put-call symmetry of powered options." J. Appl. Probab. 52 (1) 82 - 101, March 2015. https://doi.org/10.1239/jap/1429282608

Information

Published: March 2015
First available in Project Euclid: 17 April 2015

zbMATH: 1344.60074
MathSciNet: MR3336848
Digital Object Identifier: 10.1239/jap/1429282608

Subjects:
Primary: 60J25
Secondary: 60J60 , 60J75 , 62P05 , 97M30

Keywords: dual semigroup , generators of dual processes , powered and digital options , put-call symmetry and reversal , stochastic duality , Stochastic monotonicity , straddle

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 1 • March 2015
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