On a generalized optional decomposition theorem
| Autor: | Abdelkarem Berkaoui |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Statistics and Probability
Discrete mathematics Sublinear function media_common.quotation_subject Field (mathematics) Ambiguity Adapted process Set (abstract data type) Modeling and Simulation Incomplete markets Filtration (mathematics) Optimal stopping Mathematical economics media_common Mathematics |
| Zdroj: | Stochastics. 86:906-921 |
| ISSN: | 1744-2516 1744-2508 |
| DOI: | 10.1080/17442508.2014.895357 |
| Popis: | First we consider a set of probabilities and denote by , the associated dynamic sublinear expectation, defined by for and a fixed filtration . We prove that for a positive -supermartingale X, there exits an increasing adapted process C such that is a local -martingale. Second we apply such a result to incomplete market under model misspecification, generalizing the results of Kramkov [D.O. Kramkov, Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets, Prob. Theor. Relat. Field. 15 (1996), pp. 459–479] and Riedel [F. Riedel, On optimal stopping under Ambiguity, Econometrica. 77 (2009), pp. 857–908]. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|