Electronic Communications in Probability

Existence and uniqueness for backward stochastic differential equations driven by a random measure, possibly non quasi-left continuous

Elena Bandini

Full-text: Open access

Abstract

We study the following backward stochastic differential equation on finite time horizon driven by an integer-valued random measure $\mu$ on $\mathbb R_+\times E$, where $E$ is a Lusin space, with compensator $\nu(dt,dx)=dA_t\,\phi_t(dx)$:\[Y_t = \xi + \int_{(t,T]} f(s,Y_{s-},Z_s(\cdot))\, d A_s - \int_{(t,T]} \int_E Z_s(x) \, (\mu-\nu)(ds,dx),\qquad 0\leq t\leq T.\]The generator $f$ satisfies, as usual, a uniform Lipschitz condition with respect to its last two arguments. In the literature, the existence and uniqueness for the above equation in the present general setting has only been established when $A$ is continuous or deterministic. The general case, i.e. $A$ is a right-continuous nondecreasing predictable process, is addressed in this paper.

Article information

Source
Electron. Commun. Probab., Volume 20 (2015), paper no. 71, 13 pp.

Dates
Accepted: 6 October 2015
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465320998

Digital Object Identifier
doi:10.1214/ECP.v20-4348

Mathematical Reviews number (MathSciNet)
MR3407215

Zentralblatt MATH identifier
1329.60172

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60G57: Random measures

Keywords
Backward stochastic differential equations random measures

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Bandini, Elena. Existence and uniqueness for backward stochastic differential equations driven by a random measure, possibly non quasi-left continuous. Electron. Commun. Probab. 20 (2015), paper no. 71, 13 pp. doi:10.1214/ECP.v20-4348. https://projecteuclid.org/euclid.ecp/1465320998


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