A numerical algorithm for fully nonlinear HJB equations: an approach by control randomization
type: Dataset
description: We propose a probabilistic numerical algorithm to solve Backward Stochastic Differential Equations (BSDEs) with nonnegative jumps, a class of BSDEs introduced in [9] for representing fully nonlinear HJB equations. In particular, this allows us to numerically solve stochastic control problems with controlled volatility, possibly degenerate. Our backward scheme, based on least-squares regressions, takes advantage of high-dimensional properties of Monte-Carlo methods, and also provides a parametric estimate in feedback form for the optimal control. A partial analysis of the error of the scheme is provided, as well as numerical tests on the problem of superreplication of option with uncertain volatilities and/or correlations, including a detailed comparison with the numerical results from the alternative scheme proposed in [7].
issued: 2026-05-08T04:59:47.069483
language: en
modified: 2026-05-08T04:59:47.069487
contact point: Organization
  fn: CCSD
keyword: backward-stochastic-differential-equations
keyword: control-randomization
keyword: empirical-regressions
keyword: hjb-equation
keyword: infoeu-reposemanticspreprint
keyword: jel-c---mathematical-and-quantitative-methodscc6---mathematical-methods--programming-models--ma
keyword: mathmath-prmathematics-mathprobability-mathpr
keyword: monte-carlo
keyword: preprints-working-papers-
keyword: qfincpquantitative-finance-q-fincomputational-finance-q-fincp
keyword: qfinprquantitative-finance-q-finpricing-of-securities-q-finpr
keyword: uncertain-volatility
landing page: https://hal.science/hal-00905899

A numerical algorithm for fully nonlinear HJB equations: an approach by control randomization
type: Distribution
format: HTML
issued: 2026-05-08T04:59:47.071028
modified: 2026-05-08T04:59:47.053018
access URL: https://hal.science/hal-00905899

test_moissonnage_selune
type: Agent