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137
From BlackScholes and Dupire formulae to last passage times of local martingales. Part B : The finite time horizon
, 2008
"... ..."
Martingale densities for general asset prices
 Journal of Mathematical Economics
, 1992
"... Abstract: This paper discusses some properties of general asset prices in continuous time. We introduce the concept of a martingale density which is a generalization of an equivalent martingale measure, and we show that absence of arbitrage plus some technical conditions implies the existence of a ..."
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Cited by 26 (1 self)
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of a martingale density. This is in turn already su±cient to derive a recent result of Back (1990) on local risk premia for asset returns. As an application, we obtain a simple condition, valid in arbitrary information structures, for the drift part of discounted security gains to be absolutely
A minimality property of the minimal martingale measure
 Statistics and Probability Letters
, 1999
"... Abstract: Let X be a continuous adapted process for which there exists an equivalent local martingale measure (ELMM). The minimal martingale measure bP is the unique ELMM for X with the property that local Pmartingales strongly orthogonal to the Pmartingale part of X are also local bPmartingales. ..."
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Cited by 19 (0 self)
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Abstract: Let X be a continuous adapted process for which there exists an equivalent local martingale measure (ELMM). The minimal martingale measure bP is the unique ELMM for X with the property that local Pmartingales strongly orthogonal to the Pmartingale part of X are also local bPmartingales
ON SINGULAR INTEGRAL AND MARTINGALE TRANSFORMS
"... Abstract. Linear equivalences of norms of vectorvalued singular integral operators and vectorvalued martingale transforms are studied. In particular, it is shown that the UMDconstant of a Banach space X equals the norm of the real (or the imaginary) part of the BeurlingAhlfors singular integral ..."
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Cited by 20 (3 self)
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Abstract. Linear equivalences of norms of vectorvalued singular integral operators and vectorvalued martingale transforms are studied. In particular, it is shown that the UMDconstant of a Banach space X equals the norm of the real (or the imaginary) part of the BeurlingAhlfors singular integral
Strict local martingales and bubbles
"... This paper deals with asset price bubbles modeled by strict local martingales. With any strict local martingale, one can associate a new measure, which is studied in detail in the first part of the paper. In the second part, we determine the “default term ” apparent in riskneutral option prices if ..."
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Cited by 8 (0 self)
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This paper deals with asset price bubbles modeled by strict local martingales. With any strict local martingale, one can associate a new measure, which is studied in detail in the first part of the paper. In the second part, we determine the “default term ” apparent in riskneutral option prices
RiskMinimality and Orthogonality of Martingales”,
 Stochastics and Stochastics Reports
, 1990
"... Abstract: We characterize the orthogonality of martingales as a property of riskminimality under certain perturbations by stochastic integrals. The integrator can be either a martingale or a semimartingale; in the latter case, the finite variation part must be continuous. This characterization is b ..."
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Cited by 15 (2 self)
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Abstract: We characterize the orthogonality of martingales as a property of riskminimality under certain perturbations by stochastic integrals. The integrator can be either a martingale or a semimartingale; in the latter case, the finite variation part must be continuous. This characterization
Martingale Problem for (,,)Superprocesses
, 1997
"... . The martingale problem for superprocesses with parameters (¸; \Phi; k) is studied where k(ds) may not be absolutely continuous with respect to the Lebesgue measure. This requires a generalization of the concept of martingale problem: we show that for any process X which partially solves the martin ..."
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the martingale problem, an extended form of the liftings defined in [11] exists; these liftings are part of the statement of the full martingale problem, which is hence not defined for processes X who fail to solve the partial martingale problem. The existence of a solution to the martingale problem follows
Integration by Parts and Martingale Representation for a Markov Chain
"... Integrationbyparts formulas for functions of fundamental jump processes relating to a continuoustime, finitestate Markov chain are derived using Bismut's change of measures approach to Malliavin calculus. New expressions for the integrands in stochastic integrals corresponding to represent ..."
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to representations of martingales for the fundamental jump processes are derived using the integrationbyparts formulas. These results are then applied to hedge contingent claims in a Markov chain financial market, which provides a practical motivation for the developments of the integrationbyparts formulas
A Compactness Principle For Bounded Sequences Of Martingales With Applications
 PROCEEDINGS OF THE SEMINAR OF STOCHASTIC ANALYSIS, RANDOM FIELDS AND APPLICATIONS, PROGRESS IN PROBABILITY
, 1996
"... For H¹ bounded sequences, we introduce a technique, related to the KadecPełczynskidecomposition for L¹ sequences, that allows us to prove compactness theorems. Roughly speaking, a bounded sequence in H¹ can be split into two sequences, one of which is weakly compact, the other forms the singular p ..."
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Cited by 27 (4 self)
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part. If the martingales are continuous then the singular part tends to zero in the semimartingale topology. In the general case the singular parts give rise to a process of bounded variation. The technique allows to give a new proof of the optional decomposition theorem in Mathematical Finance.
Results 1  10
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137