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- W4313197228 abstract "The paper is directly motivated by the pricing of vulnerable European and American options in a general hazard process setup and a related study of the corresponding pre-default backward stochastic differential equations (BSDE) and pre-default reflected backward stochastic differential equations (RBSDE). We work with a generic filtration $FF$ for which the martingale representation property is assumed to hold with respect to a square-integrable martingale $M$ and the goal of this work is of twofold. First, we aim to establish the well-posedness results and comparison theorems for a generalized BSDE and a reflected generalized BSDE with a continuous and nondecreasing driver $A$. Second, we study extended penalization schemes for a generalized BSDE and a reflected generalized BSDE in which we penalize against the driver in order to obtain in the limit either a particular optimal stopping problem or a Dynkin game in which the set of admissible exercise time is constrained to the right support of the measure generated by $A$." @default.
- W4313197228 created "2023-01-06" @default.
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- W4313197228 date "2022-12-24" @default.
- W4313197228 modified "2023-09-27" @default.
- W4313197228 title "Well-posedness and penalization schemes for generalized BSDEs and reflected generalized BSDEs" @default.
- W4313197228 doi "https://doi.org/10.48550/arxiv.2212.12854" @default.
- W4313197228 hasPublicationYear "2022" @default.
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