Generalization of Doob Decomposition Theorem and Risk Assessment in Incomplete Markets
Abstrak
In the paper, we introduce the notion of a local regular supermartingale relative to a convex set of equivalent measures and prove for it the necessary and sufficient conditions of optional Doob decomposition in the discrete case. This Theorem is a generalization of the famous Doob decomposition onto the case of supermartingales relative to a convex set of equivalent measures. The description of all local regular supermartingales relative to a convex set of equivalent measures is presented. A notion of complete set of equivalent measures is introduced. We prove that every non negative bounded supermartingale relative to a complete set of equivalent measures is local regular. A new definition of fair price of contingent claim in incomplete market is given and a formula for fair price of Standard option of European type is found.
Penulis (1)
N. S. Gonchar
Akses Cepat
- Tahun Terbit
- 2016
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓