BSDE associated with Lévy processes and application to PDIE

By Khaled Bahlali, Mhamed Eddahbi, E. Essaky. 2003

62 citations recorded by the source corpus.

We deal with backward stochastic differential equations (BSDE for short) driven by Teugel's martingales and an independent Brownian motion. We study the existence, uniqueness and comparison of solutions for these equations under a Lipschitz as well as a locally Lipschitz conditions on the coefficient. In the locally Lipschitz case, we prove that if the Lipschitz constant LN behaves as log(N) in the ball B(0,N), then the corresponding BSDE has a unique solution which depends continuously on the on the coefficient and the terminal data. This is done with an unbounded terminal data. As application, we give a probabilistic interpretation for a large class of partial differential integral equations (PDIE for short).

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/e3be082ccd20a5c49f60445bde5d21c6384932d8

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In Finance

1. Yong Ren
2. Xiliang Fan
3. Zuomao Yan
4. Hongwu Zhang

In Management Science and Operations Research

1. Yong Ren
2. Xiliang Fan

Citations in the corpus

• REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY A LÉVY PROCESS (2008, methodology): “The predictable representation property (see [15] Proposition 2.”