On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case

By François Delarue. 2002

281 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Finance, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/9c77dd3f6144460be0591a7c6643ce0ab50eb3cd

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Citations in the corpus

A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria (2014, methodology): “For instance, following Delarue [10], we get that, for any p ě 1, we can find Γp :“ ΓppKq ą 0 (the value of which is allowed to increase from line to line), such that for γ ď 1{Γp, (4.18) holds, but with a simpler right-hand side just consisting of Γpr|η| 2p ` R2pa s.”
Control of McKean–Vlasov dynamics versus mean field games (2012, methodology): “We refer to [8] for a review of this strategy.”
Finite state mean field games with Wright–Fisher common noise (2019, methodology): “A standard strategy for solving forward-backward stochastic differential equations (at least in the so-called Markovian case, see for instance [51, 20]) is to regard the system formed by the two forward and backward equations as the characteristics of a system of parabolic second order PDEs.”
A Forward-Backward Stochastic Algorithm For Quasi-Linear PDEs (2006, methodology): “In [ 6 ] the first author overcomes the strong coupling between the forward and backward equations by solving by induction the local versions of (E )o n[tk ,t k+1], k running downward from N − 1t o 0. By analogy with this approach, the discretization procedure of the forward component on a step [tk ”
On some recent aspects of stochastic control and their applications (2005, methodology): “There are essentially two methods for proving the solvability of BSDE : pure probabilistic methods like the method of continuation, see [2], [48], and combined methods of PDE and probability like the four step scheme developed in [65], or more recently extensions in [74], [ 27 ].”
MEAN FIELD GAMES: A TOY MODEL ON AN ERDOS-RENYI GRAPH (2017, methodology): “By using the same kind of change of variable as in Section 2, we can “remove” the linear term in x in the backward component; thanks to [9], we can deduce that the above system is uniquely solvable when f and g are bounded and Lipschitz continuous.”
A Probabilistic Approach to Mean Field Games with Major and Minor Players (2014, background): “The concept of (deterministic) decoupling field lies at the core of many investigations of the well-posedness of standard FBSDEs, see for example [14, 22].”
Forward-backward systems for expected utility maximization (2011, methodology): “The treatment has focused on mainly three methods: one using contraction mappings ([1], [33]), one based on PDE ([24], [9]), and the method of continuation ([15], [38]).”
Probabilistic Analysis of Mean-Field Games (2012, background): “1 in [8], existence and uniqueness hold for small time.”
CLASSICAL SOLUTIONS TO THE MASTER EQUATION FOR LARGE POPULATION EQUILIBRIA (2014, methodology): “ion (2.5) allows us to characterize the decoupling ﬁeld of the system (2.2) as follows: CLASSICAL SOLUTIONS TO THE MASTER EQUATION 7 Under pH0q(i), we know from the classical theory of coupled FBSDEs [10] that, for T suﬃciently small, for any t P r0,Ts, there exists a continuous decoupling ﬁeld ˆut,”
Time discretization and Markovian iteration for coupled FBSDEs (2008, background): “ i,x) and ˜un , F n(u0). It is obvious that Y˜n i = ˜uni(X˜n i ). Note again that (6.1) is decoupled. By Theorem 6.1, and applying nowadays standard arguments for decoupled FBSDEs (see, e.g., Delarue [9] and Zhang [26] for (i), and Zhang [25] and Bouchard and Touzi [4] for (ii)), we can derive the f”
Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs (2005, background): “But they have been overcome, and now an impressive theory is available; see for instance, Bismut [7, 8], Arkin and Saksonov [2], Pardoux and Peng [39, 40, 41], Peng [43, 44, 45, 46, 47, 48], Antonelli [1], Ma et al. [36, 37, 38], Douglas et al. [22], Cvitani¶c et al. [17, 18, 19], Chevance [15], Par”
Weak existence and uniqueness for forward–backward SDEs (2006, methodology): “g Antonelli and Ma [2] or Delarue [7], Remark 1.”
7 – Backward Stochastic Differential Equations (2011, unknown): “In the following we use conditions of Pardoux and Tang [67] and Delarue [27].”