The Mathematics of Arbitrage

By Freddy Delbaen, Walter Schachermayer. 2006

561 citations recorded by the source corpus.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/693783d7174f677a258f798ec10d07a0fe6b1931

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Citations in the corpus

Long Term Risk: A Martingale Approach (2014, unknown): “k premium. The martingale can be conveniently used to change over to the risk-neutral probabilities (Cox and Ross (1976a), Cox and Ross (1976b), Harrison and Kreps (1979), Harrison and Pliska (1981), Delbaen and Schachermayer (2006)). Under the risk-neutral probability measure risky future payoﬀs ar”
Bid-Ask Dynamic Pricing in Financial Markets with Transaction Costs and Liquidity Risk (2007, background): “P (g0 > 0) = sup{P (g > 0), g ∈ G} As in [27], the probability measure R of Radon Nikodym derivative g0 E(g0) is equivalent to P and supX∈C ER(X) = 0.”
MINIMAL f q -MARTINGALE MEASURES FOR EXPONENTIAL LÉVY PROCESSES (2007, background): “(SC) is satisfied if there exists a d-dimensional predictable process λ with A = ∫ d〈M〉λ and K̂T := ∫ λ∗ d〈M〉λ < ∞;(3.1) see Definition 1.1 in Choulli and Stricker [3] and Section 12.3 in Delbaen and Schachermayer [5] for a related discussion.”
A Dysfunctional Role of High Frequency Trading in Electronic Markets (2012, unknown): “See for example [6],[7], or [8].”
Counterparty Risk and Funding: A Tale of Two Puzzles (2014, methodology): “In the ensuing classical risk neutral valuation framework we can proceed with presenting the following definitions, which are consistent with the standard theory of arbitrage (cf. Delbaen and Schachermayer (2006)).”
Separation and duality in locally L 0 -convex modules (2009, unknown): “[6,10].”
HEDGING UNDER ARBITRAGE (2010, unknown): “of return and volatility coefﬁcients only depend on time and on the current market conﬁguration. Since we do not rely on a mar tingale representation theorem, 1We refer the reader to the monograph by Delbaen and Schachermayer (2006) for a thorough introduction to NA, NFLVR and other notions of arbit”
HOW CLOSE ARE THE OPTION PRICING FORMULAS OF BACHELIER AND BLACK–MERTON–SCHOLES? (2007, unknown): “Mathematical Finance, Vol. 18, No. 1 (January 2008), 155–170”
MULTIFRACTIONAL STOCHASTIC VOLATILITY MODELS (2011, unknown): “[27]), such a requirement need not be imposed on instantaneous volatility.”
Arbitrage and duality in nondominated discrete-time models (2013, background): “Our main financial results are, of course, extensions of the classical case where P is a singleton; see, for example, [19, 29] and the references therein.”
The fundamental theorem of asset pricing for continuous processes under small transaction costs (2010, background): “The corresponding notion of admissibility, which compares the portfolio to the vector (1, 0) rather than to (1, 1), goes back to Harrison and Pliska [12] (compare also to [6] and [8]).”
Arbitrage‐free XVA (2016, unknown): “The admissible set of trading strategies is the class of F -predictable processes such that the portfolio process is bounded from below; see also Delbaen and Schachermayer (2006).”
Forward-backward systems for expected utility maximization (2011, methodology): “[5] J. Cvitanić, W. Schachermayer, and H. Wang.”
Convex compactness and its applications (2007, unknown): “205 in [8], we get the following estimate P[gβ ≥ nε 2 ] ≥ ε 2 , for all β βn .”