Journal of Applied Mathematics

G-Doob-Meyer Decomposition and Its Applications in Bid-Ask Pricing for Derivatives under Knightian Uncertainty

Wei Chen

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Abstract

The target of this paper is to establish the bid-ask pricing framework for the American contingent claims against risky assets with G-asset price systems on the financial market under Knightian uncertainty. First, we prove G-Dooby-Meyer decomposition for G-supermartingale. Furthermore, we consider bid-ask pricing American contingent claims under Knightian uncertainty, by using G-Dooby-Meyer decomposition; we construct dynamic superhedge strategies for the optimal stopping problem and prove that the value functions of the optimal stopping problems are the bid and ask prices of the American contingent claims under Knightian uncertainty. Finally, we consider a free boundary problem, prove the strong solution existence of the free boundary problem, and derive that the value function of the optimal stopping problem is equivalent to the strong solution to the free boundary problem.

Article information

Source
J. Appl. Math., Volume 2015 (2015), Article ID 910809, 13 pages.

Dates
First available in Project Euclid: 16 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1442420568

Digital Object Identifier
doi:10.1155/2015/910809

Mathematical Reviews number (MathSciNet)
MR3391792

Citation

Chen, Wei. G-Doob-Meyer Decomposition and Its Applications in Bid-Ask Pricing for Derivatives under Knightian Uncertainty. J. Appl. Math. 2015 (2015), Article ID 910809, 13 pages. doi:10.1155/2015/910809. https://projecteuclid.org/euclid.jam/1442420568


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