BSDEs with random terminal time under enlarged filtration American-style options hedging by an insider

Anne Eyraud-Loisel (1) , Manuela Royer-Carenzi (2)

1 SAF - Laboratoire de Sciences Actuarielle et Financière
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

Markets with asymmetrical information are generally studied from a wealth opti-mization point of view. We focus here on a hedging problem for a financial agent who has an additional information on the market. We extend the results given for hedging strategies with fixed terminal time to the case of a random terminal time. In particular, we provide tools to understand the behavior of American option hedging by an insider. To achieve this aim, we prove the existence and uniqueness of backward stochastic differential equations (BSDE) solutions, when terminal time is random, under an initially enlarged filtration.

Mots clés: enlargement of filtration; insider trading; American option hedg-ing; asymmetrical information; BSDE; uncertain time horizon

Domaines: Probabilités [math.PR]

Anne Eyraud-Loisel, Manuela Royer-Carenzi. BSDEs with random terminal time under enlarged filtration American-style options hedging by an insider. Random Operators and Stochastic Equations, 2009, 17, pp.12-30. ⟨hal-01107366⟩