Backward Stochastic Differential Equations Driven By Càdlàg Martingales

Carbone, Raffaella; Ferrario, Benedetta; Santacroce, Marina

doi:10.1137/s0040585x97983055

Cited by 71 publications

(134 citation statements)

References 13 publications

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“…A series of works [16,30,32,15,18,56,19] are dedicated to the theory of BSDEs (1.3) but driven by a càdlàg martingale under a right-continuous filtration that is also quasi-left continuous. Lately, [12,62] removed the quasileft continuity assumption from the filtration so that the quadratic variation of the driving martingale does not need to be absolutely continuous.…”

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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“…Existence and uniqueness of the solution to (3.3) follows from Carbone et al [6]. Notice that the processL in (3.3) is necessary for the existence of the solution since the predictable representation property does not hold in the discrete case (see e.g.…”

Section: Discrete-time Modelmentioning

confidence: 96%

“…The existence and uniqueness of the solution to (2.5) are well studied in Carbone et al [6] for general square integrable martingales M not necessarily of the form we impose. We mention that their study does not include the dependence on S in the functions h and ϕ .…”

Section: Continuous-time Modelmentioning

confidence: 97%

“…From Carbone et al [6], we know that the solution to (5.1) exists and is unique. Notice that L ε (T ) is an G T -measurable square integrable random variable.…”

Section: 1mentioning

confidence: 99%

“…A solution to the backward equation in (1.1) is a triplet (V, Υ, L). We refer to Carbone et al [6] for the study of the existence and uniqueness of this solution.…”

Section: υ(S) Dm (S) − L(t ) + L(t) mentioning

confidence: 99%

See 2 more Smart Citations

Discretisation of FBSDEs driven by càdlàg martingales

Khedher¹,

Vanmaele

2016

Journal of Mathematical Analysis and Applications

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Hedging and utility valuation of a defaultable claim driven by Hawkes processes

Pasricha

Selvamuthu

Tardelli

2021

Appl Stoch Models Bus & Ind

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This article studies the problem of hedging a defaultable claim via the maximization of the mean value of exponential utility, over a set of admissible strategies. The dynamics of the underlying asset is assumed to be governed by mutually exciting Hawkes processes, which captures the jumps clustering phenomenon observed in the market. The resulting market is incomplete and does not allow perfect replication. Hence, a dynamic programming approach is adopted to characterize the value function as the largest solution to a suitable backward stochastic differential equation (BSDE) with a non‐Lipschitz generator. The value function of the optimal investment problem and of the indifference prices are represented in terms of limits of the sequence of value functions of suitable Lipschitz BSDEs and, further, a result of uniqueness is achieved. Finally, numerical experiments are performed to demonstrate the applicability of the proposed framework and to understand the impact of the jump‐clustering on the values of the claims.

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Backward Stochastic Differential Equations Driven By Càdlàg Martingales

Cited by 71 publications

References 13 publications

Lp solutions of backward stochastic differential equations with jumps

Lp solutions of backward stochastic differential equations with jumps

Discretisation of FBSDEs driven by càdlàg martingales

Hedging and utility valuation of a defaultable claim driven by Hawkes processes

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