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Explicit form and path regularity of martingale representations. (English) Zbl 0979.60027

Barndorff-Nielsen, Ole E. (ed.) et al., Lévy processes. Theory and applications. Boston: Birkhäuser. 337-360 (2001).
Let \(X\) denote the solution of a stochastic differential equation driven by a Wiener process and a compensated Poisson random measure, and assume that \(X\) is an \(L\)-square martingale. Let \(\Phi(X)\) denote a given functional of \(X\) defined as an integral with respect to \(dX\). The paper gives sufficient conditions on \(\Phi\) in order that the integrand be left-continuous with right limits. This result may find application in mathematical finance.
For the entire collection see [Zbl 0961.00012].

MSC:

60G44 Martingales with continuous parameter
60H20 Stochastic integral equations
60H30 Applications of stochastic analysis (to PDEs, etc.)
91B28 Finance etc. (MSC2000)
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