8. ON SIGNED ADMISSIBLE MARTINGALE DEFORMATIONS
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