G-Doob-Meyer Decomposition and Its Applications in Bid-Ask Pricing for Derivatives under Knightian Uncertainty
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 b...
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Wiley
2015-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/910809 |
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| author | Wei Chen |
| author_facet | Wei Chen |
| author_sort | Wei Chen |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-49d0a62d49ed43e7b88029bd4db96969 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-49d0a62d49ed43e7b88029bd4db969692025-02-03T01:30:08ZengWileyJournal of Applied Mathematics1110-757X1687-00422015-01-01201510.1155/2015/910809910809G-Doob-Meyer Decomposition and Its Applications in Bid-Ask Pricing for Derivatives under Knightian UncertaintyWei Chen0School of Economics, Shandong University, Jinan 250100, ChinaThe 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.http://dx.doi.org/10.1155/2015/910809 |
| spellingShingle | Wei Chen G-Doob-Meyer Decomposition and Its Applications in Bid-Ask Pricing for Derivatives under Knightian Uncertainty Journal of Applied Mathematics |
| title | G-Doob-Meyer Decomposition and Its Applications in Bid-Ask Pricing for Derivatives under Knightian Uncertainty |
| title_full | G-Doob-Meyer Decomposition and Its Applications in Bid-Ask Pricing for Derivatives under Knightian Uncertainty |
| title_fullStr | G-Doob-Meyer Decomposition and Its Applications in Bid-Ask Pricing for Derivatives under Knightian Uncertainty |
| title_full_unstemmed | G-Doob-Meyer Decomposition and Its Applications in Bid-Ask Pricing for Derivatives under Knightian Uncertainty |
| title_short | G-Doob-Meyer Decomposition and Its Applications in Bid-Ask Pricing for Derivatives under Knightian Uncertainty |
| title_sort | g doob meyer decomposition and its applications in bid ask pricing for derivatives under knightian uncertainty |
| url | http://dx.doi.org/10.1155/2015/910809 |
| work_keys_str_mv | AT weichen gdoobmeyerdecompositionanditsapplicationsinbidaskpricingforderivativesunderknightianuncertainty |