The play operator, the truncated variation and the generalisation of the Jordan decomposition

DOI10.1002/mma.3077zbMath1307.60028arXiv1311.6405OpenAlexW3105895991MaRDI QIDQ5178132

Raouf Ghomrasni, Rafał Marcin Łochowski

Publication date: 13 March 2015

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.6405

zbMATH Keywords

Skorokhod problemrate independenceplay operatortruncated variationcontinuity of the play operator

Mathematics Subject Classification ID

Strong limit theorems (60F15) Martingales with continuous parameter (60G44) Sample path properties (60G17) Functional limit theorems; invariance principles (60F17)

Related Items (6)

Quadratic variation of a càdlàg semimartingale as a.s. limit of the normalized truncated variations ⋮ A new theorem on the existence of the Riemann-Stieltjes integral and an improved version of the Loéve-Young inequality ⋮ On optimal uniform approximation of Lévy processes on Banach spaces with finite variation processes ⋮ On the double Laplace transform of the truncated variation of a Brownian motion with drift ⋮ On reflected stochastic differential equations driven by regulated semimartingales ⋮ A new inequality for the Riemann-Stieltjes integrals driven by irregular signals in Banach spaces

Cites Work

• Truncated variation, upward truncated variation and downward truncated variation of Brownian motion with drift -- their characteristics and applications
• The Skorokhod problem in a time-dependent interval
• Differential models of hysteresis
• Duality in the space of regulated functions and the play operator
• On BV-type hysteresis operators
• On truncated variation, upward truncated variation and downward truncated variation for diffusions
• A tree approach to \(p\)-variation and to integration
• On a generalisation of the Hahn–Jordan decomposition for real càdlàg functions
• Efficient analytic approximation of the optimal hedging strategy for a European call option with transaction costs
• The play operator on the rectifiable curves in a Hilbert space
• Hysteresis systems with variable characteristics
• Optimal hedging of options with small but arbitrary transaction cost structure
• An Asymptotic Analysis of an Optimal Hedging Model for Option Pricing with Transaction Costs

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