1
|
Carmona R, Laurière M. Convergence analysis of machine learning algorithms for the numerical solution of mean field control and games: II—the finite horizon case. ANN APPL PROBAB 2022. [DOI: 10.1214/21-aap1715] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- René Carmona
- Department of Operations Research and Financial Engineering, Princeton University
| | - Mathieu Laurière
- Department of Operations Research and Financial Engineering, Princeton University
| |
Collapse
|
2
|
|
3
|
Mean square rate of convergence for random walk approximation of forward-backward SDEs. ADV APPL PROBAB 2020. [DOI: 10.1017/apr.2020.17] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
AbstractLet (Y,Z) denote the solution to a forward-backward stochastic differential equation (FBSDE). If one constructs a random walk$B^n$from the underlying Brownian motionBby Skorokhod embedding, one can show$L_2$-convergence of the corresponding solutions$(Y^n,Z^n)$to$(Y, Z).$We estimate the rate of convergence based on smoothness properties, especially for a terminal condition function in$C^{2,\alpha}$. The proof relies on an approximative representation of$Z^n$and uses the concept of discretized Malliavin calculus. Moreover, we use growth and smoothness properties of the partial differential equation associated to the FBSDE, as well as of the finite difference equations associated to the approximating stochastic equations. We derive these properties by probabilistic methods.
Collapse
|
4
|
Backhoff-Veraguas J, Lacker D, Tangpi L. Nonexponential Sanov and Schilder theorems on Wiener space: BSDEs, Schrödinger problems and control. ANN APPL PROBAB 2020. [DOI: 10.1214/19-aap1531] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
5
|
Geiss C, Labart C, Luoto A. Random walk approximation of BSDEs with Hölder continuous terminal condition. BERNOULLI 2020. [DOI: 10.3150/19-bej1120] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|