BSDEs with monotone generator and two irregular reflecting barriers

Klimsiak, Tomasz

doi:10.1016/j.bulsci.2012.06.006

Cited by 45 publications

(74 citation statements)

References 32 publications

(54 reference statements)

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“…However, their wellposedness result requires a relatively stronger monotone condition and Lipschitz continuity of f in z see (H1) and (H3) therein . Klimsiak studied L p solutions of reflected BSDEs under a general right-continuous filtration in [49], and analyzed L p solutions to BSDEs with monotone generators and two irregular reflecting barriers in [48].…”

Section: Introductionmentioning

confidence: 99%

Lp solutions of backward stochastic differential equations with jumps

Yao

2017

Stochastic Processes and their Applications

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Given p ∈ (1, 2), we study L p solutions of a multi-dimensional backward stochastic differential equation with jumps (BSDEJ) whose generator may not be Lipschitz continuous in (y, z)−variables. We show that such a BSDEJ with p−integrable terminal data admits a unique L p solution by approximating the monotonic generator by a sequence of Lipschitz generators via convolution with mollifiers and using a stability result.

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Section: Introductionmentioning

confidence: 99%

Lp solutions of backward stochastic differential equations with jumps

Yao

2017

Stochastic Processes and their Applications

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“…✷ To prove the existence result for (1.5) we will need the monotone convergence theorem for BSDEs stated below. In the case of Brownian filtration this result was proved in [17,28]. In the case of general filtration it follows from [19].…”

Section: Existence Of Solutionsmentioning

confidence: 86%

Systems of quasi-variational inequalities related to the switching problem

Klimsiak

2019

Stochastic Processes and their Applications

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We prove the existence of weak solution for a system of quasi-variational inequalities related to a switching problem with dynamic driven by operator associated with a semi-Dirichlet form and with measure data. We give a stochastic representation of solutions in terms of solutions of a system of reflected BSDEs with oblique reflection. As a by-product, we prove the existence of an optimal strategy in the switching problem and show regularity of the payoff function. (2010): 35J75, 60J45. Mathematics Subject Classification

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“…Thus we do not give all details but we point out the differences. Let us remark that our condition H4 on the growth of the driver f or the integrability assumption C1 on the terminal value ξ and f 0 are not optimal, compared to the conditions imposed in [22] for example (see also among others [23,24,29] for reflected BSDE with monotone generator). This improvement of our result would be quite long and is left for further research.…”

Section: Reflected Bsde With Monotone Drivermentioning

confidence: 95%