Explicit form and robustness of martingale representations

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Pricing and Hedging in Exponential Lévy Models: Review of Recent Results (2011, background): “Formulas for φ H t with various degrees of explicitness and under various assumptions on the driving process X and on the pay-off G were given in [9, 20, 6, 27] and several other papers.”
Asymptotic analysis of hedging errors in models with jumps (2009, background): “Schweizer [6] up to more recent works [4,14,17,20].”
Arbitrage in continuous complete markets (2002, background): “Note that the assumptions in Theorem 3.3 can be relaxed; see Jacod et al. (2000).”
Hedging with options in models with jumps (2007, background): “• When X is a martingale, problem (3) is related to the Kunita-Watanabe decomposition of Y , which has well-known properties guaranteeing the existence of a solution under mild conditions [22].”
Path regularity for solutions of backward stochastic differential equations (2002, background): “In a recent paper Jacod-Méléard-Protter [2] studied, among other things, the explicit form and path regularity of Z, as a “martingale representation” problem when W is allowed to be any Lévy process and g is continuously differentiable.”