Martingale representation for Poisson processes with applications to minimal variance hedging

DOI10.1016/j.spa.2011.03.014zbMath1219.60050arXiv1001.3972OpenAlexW2116082192MaRDI QIDQ550168

Günter Last, Mathew D. Penrose

Publication date: 8 July 2011

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.3972

zbMATH Keywords

Malliavin calculusClark-Ocone formulaPoisson processmartingale representationderivative operatorindependent random measureKunita-Watanabe decompositionminimal variance hedge

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Martingales with continuous parameter (60G44) Financial applications of other theories (91G80) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (8)

\(L_{2}\)-variation of Lévy driven BSDEs with non-smooth terminal conditions ⋮ Malliavin calculus for marked binomial processes and applications ⋮ Stochastic Analysis for Poisson Processes ⋮ The random connection model and functions of edge-marked Poisson processes: second order properties and normal approximation ⋮ Poisson process Fock space representation, chaos expansion and covariance inequalities ⋮ Functional inequalities for marked point processes ⋮ Transportation inequalities for non-globally dissipative SDEs with jumps via Malliavin calculus and coupling ⋮ Time-dynamic evaluations under non-monotone information generated by marked point processes

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