On stochastic calculus related to financial assets without semimartingales

DOI10.1016/j.bulsci.2011.06.008zbMath1233.91337arXiv1102.2050OpenAlexW1968906272MaRDI QIDQ645948

Cristina Di Girolami, Francesco Russo, Rosanna Coviello

Publication date: 11 November 2011

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.2050

zbMATH Keywords

hedgingutility maximizationviabilityno-arbitrage\(\mathcal{A}\)-martingaleadmissible portfoliocontingent claim of interestinsiderno-semimartingaleself-financing portfolioweak \(k\)-order Brownian motion

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Microeconomic theory (price theory and economic markets) (91B24) Generalizations of martingales (60G48) Financial applications of other theories (91G80) Stochastic integrals (60H05) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (9)

GENERALIZED COVARIATION AND EXTENDED FUKUSHIMA DECOMPOSITION FOR BANACH SPACE-VALUED PROCESSES: APPLICATIONS TO WINDOWS OF DIRICHLET PROCESSES ⋮ Rough paths and symmetric-Stratonovich integrals driven by singular covariance Gaussian processes ⋮ The covariation for Banach space valued processes and applications ⋮ Generalized covariation for Banach space valued processes, Itō formula and applications ⋮ Stochastic systems with memory and jumps ⋮ A Feynman-Kac result via Markov BSDEs with generalised drivers ⋮ Pathwise stochastic integrals for model free finance ⋮ Forward integration, convergence and non-adapted pointwise multipliers ⋮ Financial economics without probabilistic prior assumptions

Cites Work

• Unnamed Item
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• Generalized covariation for Banach space valued processes, Itō formula and applications
• Clark-Ocone type formula for non-semimartingales with finite quadratic variation
• Nonsemimartingales: stochastic differential equations and weak Dirichlet processes
• No arbitrage without semimartingales
• Stochastic calculus with anticipating integrands
• Introduction to the theory of (non-symmetric) Dirichlet forms
• Robust option replication for a Black-Scholes model extended with nondeterministic trends
• Forward, backward and symmetric stochastic integration
• A general version of the fundamental theorem of asset pricing
• Arbitrage in fractional Brownian motion models
• On weak Brownian motions of arbitrary order
• Itô's formula for \(C^{1,\lambda}\)-functions of a càdlàg process and related calculus
• Additional logarithmic utility of an insider
• Tolerance to arbitrage
• Generalized integration and stochastic ODEs
• Minimal variance hedging for fractional Brownian motion
• The generalized covariation process and Itô formula
• Ito formula for \(C^ 1\)-functions of semimartingales
• Probabilistic representation for solutions of an irregular porous media type equation
• Pricing by hedging and no-arbitrage beyond semimartingales
• Consistent price systems and face-lifting pricing under transaction costs
• Finite utility on financial markets with asymmetric information and structure properties of the price dynamics
• A note on Wick products and the fractional Black-Scholes model
• A general stochastic calculus approach to insider trading
• The mathematics of arbitrage
• On bifractional Brownian motion
• LONG RANGE DEPENDENCE, NO ARBITRAGE AND THE BLACK–SCHOLES FORMULA
• Anticipative portfolio optimization
• Comment détecter le délit d'initiés?
• Arbitrage with Fractional Brownian Motion
• An Anticipating Calculus Approach to the Utility Maximization of an Insider
• Stochastic calculus with respect to continuous finite quadratic variation processes
• Elements of Stochastic Calculus via Regularization
• NO ARBITRAGE UNDER TRANSACTION COSTS, WITH FRACTIONAL BROWNIAN MOTION AND BEYOND
• Estimation of integrated volatility in stochastic volatility models

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