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

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  • Wei Chen

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.

Suggested Citation

  • Wei Chen, 2015. "G‐Doob‐Meyer Decomposition and Its Applications in Bid‐Ask Pricing for Derivatives under Knightian Uncertainty," Journal of Applied Mathematics, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnljam:v:2015:y:2015:i:1:n:910809
    DOI: 10.1155/2015/910809
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    References listed on IDEAS

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    1. Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
    2. RØdiger Frey, 2000. "Superreplication in stochastic volatility models and optimal stopping," Finance and Stochastics, Springer, vol. 4(2), pages 161-187.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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