8. ON SIGNED ADMISSIBLE MARTINGALE DEFORMATIONS


Author:  NATALIA NEUMERZHITSKAIA, IGOR PAVLOV                                                                 DOWNLOAD                                                                                                                                                                                                                                                                                   


How to Cite:




Neumerzhitskaia, Natalia, and Igor Pavlov. "On Signed Admissible Martingale Deformations." Global and

Stochastic Analysis, vol. 12, no. 5, 2025, pp. 59–66.



Abstract



Currently, the development of the theory of Haar interpolations of financial markets with the use of martingale

measures continues. The existence of martingale measures of discounted stock prices means that this kind

of interpolation can only be used in arbitrage-free markets (c.f. the survey [1]). However, real financial markets often

contain elements of arbitrage opportunities. Therefore, it is important to develop techniques for interpolating

processes that do not admit martingale measures. The work [2] is devoted to just this problem, where signed

martingale measures serve as the main interpolation tool. In this paper, we proceed to consider admissible signed

martingale deformations (in particular, their existence). Various other facts about processes on deform structures are

contained in the works [3]–[13])



Keywords


Key words and phrases. Martingale measure, deformations of the 1-st and the 2-nd kind, admissible martingale

deformations, signed deformations, binary filtration, F-admissible signed martingale deformation