Backward stochastic differential equations with jumps and related non-linear expectations

By M. Royer. 2006

250 citations recorded by the source corpus.

In this paper, we are interested in real-valued backward stochastic differential equations with jumps together with their applications to non-linear expectations. The notion of non-linear expectations has been studied only when the underlying filtration is given by a Brownian motion and in this work the filtration will be generated by both a Brownian motion and a Poisson random measure. We study at first backward stochastic differential equations driven by a Brownian motion and a Poisson random measure and then introduce the notions of f-expectations and of non-linear expectations in this set-up.

Subfields: Demography, Finance

View Paper: https://www.semanticscholar.org/paper/3bba84a301641ed96b2e53760be792443331840b

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Citations in the corpus

A new existence result for quadratic BSDEs with jumps with application to the utility maximization problem (2010, methodology): “Using both the Lipschitz property, the monotonicity of (f 1;m), the property (H2) and the comparison result in Theorem 2.5 in [ ROY06 ], (Y 1;m) is increasing and hence, we can dene ~”
On Malliavin's differentiability of BSDEs with time delayed generators driven by Brownian motions and Poisson random measures (2010, background): “BSDE without time delays and driven by Poisson random measures have already been thoroughly investigated in the literature, see [5], [6] or [23].”
Exponential Utility Maximization in an Incomplete Market with Defaults (2011, unknown): “5 in Royer [34]) can be applied.”
Reflected and doubly reflected BSDEs with jumps: A priori estimates and comparison (2008, background): “6, page 63 (see also Royer [31]) for classic BSDEs (without barriers).”
Reflected BSDEs and robust optimal stopping for dynamic risk measures with jumps (2012, unknown): “We refer to [3, 21] and to [20] where some results are used in this paper.”
Existence and Comparisons for BSDEs in general spaces (2010, unknown): “When the filtration is generated by a Poisson random measure over a separable space and a Brownian motion, as in [2], [22] and others, or by a Markov chain, as in [4], [6], we have a similar reduction.”
Reflected Backward Stochastic Differential Equation with Jumps and RCLL Obstacle (2008, background): “Fix a nonnegative constants ";‐, thanks to Appendix in [ 16 ] there exist predictable times aek;?k;k = 0;1;:::N such that ]aej;?j]\]aei;?i] = ;, 8j 6= i and”
Generalized Dynkin games and doubly reflected BSDEs with jumps (2013, unknown): “We now easily show an E-Doob-Meyer decomposition of E-supermartingales, which generalizes the results given in [37] under stronger assumptions.”
Backward SDEs with constrained jumps and quasi-variational inequalities (2008, methodology): “5 of [20], and obtain that K/1 < F*+1, 0 < t < 7\ a.”
BSDEs with jumps, optimization and applications to dynamic risk measures (2013, unknown): “This proposition corresponds to Theorem 4.6 in [25], here written in terms of risk measures.”