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## On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman Equations

ESAIM: M2AN, 36 1 (2002) 33-54

## Piecewise constant policy approximations to Hamilton–Jacobi–Bellman equations

C. Reisinger and P.A. Forsyth
Applied Numerical Mathematics 103 27 (2016)
DOI: 10.1016/j.apnum.2016.01.001

## Large time behavior for some nonlinear degenerate parabolic equations

Olivier Ley and Vinh Duc Nguyen
Journal de Mathématiques Pures et Appliquées 102 (2) 293 (2014)
DOI: 10.1016/j.matpur.2013.11.010

## A Bellman approach for two-domains optimal control problems in ℝN

G. Barles, A. Briani and E. Chasseigne
ESAIM: Control, Optimisation and Calculus of Variations 19 (3) 710 (2013)
DOI: 10.1051/cocv/2012030

## Convergence of a semi-discretization scheme for the Hamilton–Jacobi equation: A new approach with the adjoint method

F. Cagnetti, D. Gomes and H.V. Tran
Applied Numerical Mathematics 73 2 (2013)
DOI: 10.1016/j.apnum.2013.05.004

## Error estimates for second order Hamilton-Jacobi-Bellman equations. Approximation of probabilistic reachable sets

Hasnaa Zidani, Olivier Bokanowski and Mohamed Assellaou
Discrete and Continuous Dynamical Systems 35 (9) 3933 (2015)
DOI: 10.3934/dcds.2015.35.3933

## Mutual Funds Theorem for Continuous Time Markets

Nikolai Dokuchaev
SSRN Electronic Journal (2010)
DOI: 10.2139/ssrn.1591786

## Probability and Analysis in Interacting Physical Systems

G. T. Kossioris, M. Loulakis and P. E. Souganidis
Springer Proceedings in Mathematics & Statistics, Probability and Analysis in Interacting Physical Systems 283 49 (2019)
DOI: 10.1007/978-3-030-15338-0_3

## Some regularity and convergence results for parabolic Hamilton-Jacobi-Bellman equations in bounded domains

Athena Picarelli, Christoph Reisinger and Julen Rotaetxe Arto
Journal of Differential Equations 268 (12) 7843 (2020)
DOI: 10.1016/j.jde.2019.11.081

## Continuous dependence results for non-linear Neumann type boundary value problems

Espen R. Jakobsen and Christine A. Georgelin
Journal of Differential Equations 245 (9) 2368 (2008)
DOI: 10.1016/j.jde.2008.07.003

## Merton Problem with Taxes: Characterization, Computation, and Approximation

Imen Ben Tahar, H. Mete Soner and Nizar Touzi
SIAM Journal on Financial Mathematics 1 (1) 366 (2010)
DOI: 10.1137/080742178

## On Finite-Difference Approximations for Normalized Bellman Equations

István Gyöngy and David Šiška
Applied Mathematics and Optimization 60 (3) 297 (2009)
DOI: 10.1007/s00245-009-9082-0

## Convergence rates of symplectic Pontryagin approximations in optimal control theory

Mattias Sandberg and Anders Szepessy
ESAIM: Mathematical Modelling and Numerical Analysis 40 (1) 149 (2006)
DOI: 10.1051/m2an:2006002

## Convergence Rates for Semi-Discrete Splitting Approximations for Degenerate Parabolic Equations with Source Terms

E. R. Jakobsen and K. H. Karlsen
BIT Numerical Mathematics 45 (1) 37 (2005)
DOI: 10.1007/s10543-005-2641-0

## On the Rate of Convergence of Finite-Difference Approximations for Elliptic Isaacs Equations in Smooth Domains

N. V. Krylov
Communications in Partial Differential Equations 40 (8) 1393 (2015)
DOI: 10.1080/03605302.2015.1029074

## (Almost) Everything you always wanted to know about deterministic control problems in stratified domains

Guy Barles and Emmanuel Chasseigne
Networks and Heterogeneous Media 10 (4) 809 (2015)
DOI: 10.3934/nhm.2015.10.809

## Continuous dependence estimates for viscosity solutions of integro-PDEs

Espen R. Jakobsen and Kenneth H. Karlsen
Journal of Differential Equations 212 (2) 278 (2005)
DOI: 10.1016/j.jde.2004.06.021

## Abel-type Results for Controlled Piecewise Deterministic Markov Processes

Dan Goreac and Oana-Silvia Serea
Differential Equations and Dynamical Systems 25 (1) 83 (2017)
DOI: 10.1007/s12591-015-0245-y

## Linearization Techniques for Controlled Piecewise Deterministic Markov Processes; Application to Zubov’s Method

Dan Goreac and Oana-Silvia Serea
Applied Mathematics & Optimization 66 (2) 209 (2012)
DOI: 10.1007/s00245-012-9169-x

## An approximation scheme for stochastic controls in continuous time

Yumiharu Nakano
Japan Journal of Industrial and Applied Mathematics 31 (3) 681 (2014)
DOI: 10.1007/s13160-014-0157-1

## Convergence rates of Markov chain approximation methods for controlled diffusions with stopping

Qingshuo Song and Gang George Yin
Journal of Systems Science and Complexity 23 (3) 600 (2010)
DOI: 10.1007/s11424-010-0148-5

## Stochastic Optimal Control and Linear Programming Approach

R. Buckdahn, D. Goreac and M. Quincampoix
Applied Mathematics & Optimization 63 (2) 257 (2011)
DOI: 10.1007/s00245-010-9120-y

## On the convergence rate in multiscale homogenization of fully nonlinear elliptic problems

Fabio Camilli and Claudio Marchi
Networks and Heterogeneous Media 6 (1) 61 (2011)
DOI: 10.3934/nhm.2011.6.61

## Rates of convergence in periodic homogenization of fully nonlinear uniformly elliptic PDEs

Fabio Camilli and Claudio Marchi
Nonlinearity 22 (6) 1481 (2009)
DOI: 10.1088/0951-7715/22/6/011

## On the Rate of Convergence of the Finite-Difference Approximations for Parabolic Bellman Equations with Constant Coefficients

Jun Luo and N. V. Krylov
Applied Mathematics and Optimization 58 (3) 315 (2008)
DOI: 10.1007/s00245-008-9037-x

## Existence of Asymptotic Values for Nonexpansive Stochastic Control Systems

Rainer Buckdahn, Dan Goreac and Marc Quincampoix
Applied Mathematics & Optimization 70 (1) 1 (2014)
DOI: 10.1007/s00245-013-9230-4

## A Finite Element Like Scheme for Integro-Partial Differential Hamilton–Jacobi–Bellman Equations

Fabio Camilli and Espen R. Jakobsen
SIAM Journal on Numerical Analysis 47 (4) 2407 (2009)
DOI: 10.1137/080723144

## Subsolutions That Are Close in the Uniform Norm Are Close in the Sobolev Norm as Well

Muhammad Shoaib Saleem and Malkhaz Shashiashvili
Applied Mathematics & Optimization 66 (1) 1 (2012)
DOI: 10.1007/s00245-012-9161-5

## On the Rate of Convergence of Difference Approximations for Uniformly Nondegenerate Elliptic Bellman’s Equations

N. V. Krylov
Applied Mathematics & Optimization 69 (3) 431 (2014)
DOI: 10.1007/s00245-013-9228-y

## Implications of a regime-switching model on natural gas storage valuation and optimal operation

Zhuliang Chen† and Peter A. Forsyth
Quantitative Finance 10 (2) 159 (2010)
DOI: 10.1080/14697680802374791

## Error estimates for approximations of nonhomogeneous nonlinear uniformly elliptic equations

Olga Turanova
Calculus of Variations and Partial Differential Equations 54 (3) 2939 (2015)
DOI: 10.1007/s00526-015-0890-6

## Numerical analysis of strongly nonlinear PDEs

Michael Neilan, Abner J. Salgado and Wujun Zhang
Acta Numerica 26 137 (2017)
DOI: 10.1017/S0962492917000071

## Duality-based a posteriori error estimates for some approximation schemes for optimal investment problems

Athena Picarelli and Christoph Reisinger
Computers & Mathematics with Applications 79 (7) 2099 (2020)
DOI: 10.1016/j.camwa.2019.12.010

## Error estimates for approximate solutions to Bellman equations associated with controlled jump-diffusions

Espen R. Jakobsen, Kenneth H. Karlsen and Claudia La Chioma
Numerische Mathematik 110 (2) 221 (2008)
DOI: 10.1007/s00211-008-0160-z

## Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks

Dan Goreac
ESAIM: Control, Optimisation and Calculus of Variations 18 (2) 401 (2012)
DOI: 10.1051/cocv/2010103

## Linearization techniques for $\mathbb{L}^{\infty}$-control problems and dynamic programming principles in classical and $\mathbb{L}^{\infty}$-control problems

Dan Goreac and Oana-Silvia Serea
ESAIM: Control, Optimisation and Calculus of Variations 18 (3) 836 (2012)
DOI: 10.1051/cocv/2011183

## A probabilistic numerical method for fully nonlinear parabolic PDEs

Arash Fahim, Nizar Touzi and Xavier Warin
The Annals of Applied Probability 21 (4) (2011)
DOI: 10.1214/10-AAP723

## Some Applications of Linear Programming Formulations in Stochastic Control

Dan Goreac and Oana-Silvia Serea
Journal of Optimization Theory and Applications 155 (2) 572 (2012)
DOI: 10.1007/s10957-012-0080-z

## Optimal Production Control of Hybrid Manufacturing/Remanufacturing Failure-Prone Systems under Diffusion-Type Demand

Samir Ouaret, Vladimir Polotski, Jean-Pierre Kenné and Ali Gharbi
Applied Mathematics 04 (03) 550 (2013)
DOI: 10.4236/am.2013.43079

## The non-locality of Markov chain approximations to two-dimensional diffusions

C. Reisinger
Mathematics and Computers in Simulation 143 176 (2018)
DOI: 10.1016/j.matcom.2016.06.001

## The problem of optimal control with reflection studied through a linear optimization problem stated on occupational measures

Marc Quincampoix and Oana Silvia Serea
Nonlinear Analysis: Theory, Methods & Applications 72 (6) 2803 (2010)
DOI: 10.1016/j.na.2009.11.024

## A fast algorithm for the two dimensional HJB equation of stochastic control

J. Frédéric Bonnans, Élisabeth Ottenwaelter and Housnaa Zidani
ESAIM: Mathematical Modelling and Numerical Analysis 38 (4) 723 (2004)
DOI: 10.1051/m2an:2004034

## A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs

Luis A. Caffarelli and Panagiotis E. Souganidis
Communications on Pure and Applied Mathematics 61 (1) 1 (2008)
DOI: 10.1002/cpa.20208

## High-order filtered schemes for time-dependent second order HJB equations

Olivier Bokanowski, Athena Picarelli and Christoph Reisinger
ESAIM: Mathematical Modelling and Numerical Analysis 52 (1) 69 (2018)
DOI: 10.1051/m2an/2017039

## A Piecewise Deterministic Markov Toy Model for Traffic/Maintenance and Associated Hamilton–Jacobi Integrodifferential Systems on Networks

Dan Goreac, Magdalena Kobylanski and Miguel Martinez
Applied Mathematics & Optimization 74 (2) 375 (2016)
DOI: 10.1007/s00245-015-9319-z

## On the Root Solution to the Skorokhod Embedding Problem Given Full Marginals

Alexandre Richard, Xiaolu Tan and Nizar Touzi
SIAM Journal on Control and Optimization 58 (4) 1874 (2020)
DOI: 10.1137/18M1222594

## Mayer and optimal stopping stochastic control problems with discontinuous cost

Dan Goreac and Oana-Silvia Serea
Journal of Mathematical Analysis and Applications 380 (1) 327 (2011)
DOI: 10.1016/j.jmaa.2011.02.039

## Rate of convergence of finite difference approximations for degenerate ordinary differential equations

Jianfeng Zhang
Mathematics of Computation 75 (256) 1755 (2006)
DOI: 10.1090/S0025-5718-06-01876-X

## An analytical solution for the HJB equation arising from the Merton problem

Song-Ping Zhu and Guiyuan Ma
International Journal of Financial Engineering 05 (01) 1850008 (2018)
DOI: 10.1142/S2424786318500081

## NUMERICAL SOLUTIONS FOR THE CHERIDITO-SONER-TOUZI SUPER-REPLICATION MODEL UNDER GAMMA CONSTRAINTS

AGNÈS TOURIN
International Journal of Theoretical and Applied Finance 09 (03) 401 (2006)
DOI: 10.1142/S0219024906003561

## Error Estimates for Numerical Approximation of Hamilton–Jacobi Equations Related to Hybrid Control Systems

R. Ferretti, A. Sassi and H. Zidani
Applied Mathematics & Optimization 83 (1) 139 (2021)
DOI: 10.1007/s00245-018-9515-8

## Error Bounds for Monotone Approximation Schemes for Hamilton--Jacobi--Bellman Equations

Guy Barles and Espen R. Jakobsen
SIAM Journal on Numerical Analysis 43 (2) 540 (2005)
DOI: 10.1137/S003614290343815X

## Rates of Convergence of Numerical Methods for Controlled Regime-Switching Diffusions with Stopping Times in the Costs

Q. S. Song and G. Yin
SIAM Journal on Control and Optimization 48 (3) 1831 (2009)
DOI: 10.1137/070679843

## Stochastic control with rough paths

Joscha Diehl, Peter K. Friz and Paul Gassiat
Applied Mathematics & Optimization 75 (2) 285 (2017)
DOI: 10.1007/s00245-016-9333-9

## Probabilistic error analysis for some approximation schemes to optimal control problems

Athena Picarelli and Christoph Reisinger
Systems & Control Letters 137 104619 (2020)
DOI: 10.1016/j.sysconle.2019.104619

## An Error Estimate for a New Scheme for Mean Curvature Motion

SIAM Journal on Numerical Analysis 46 (5) 2715 (2008)
DOI: 10.1137/060678282

## Penalty Methods for the Solution of Discrete HJB Equations—Continuous Control and Obstacle Problems

J. H. Witte and C. Reisinger
SIAM Journal on Numerical Analysis 50 (2) 595 (2012)
DOI: 10.1137/110835840

## ON THE RATE OF CONVERGENCE OF APPROXIMATION SCHEMES FOR BELLMAN EQUATIONS ASSOCIATED WITH OPTIMAL STOPPING TIME PROBLEMS

Mathematical Models and Methods in Applied Sciences 13 (05) 613 (2003)
DOI: 10.1142/S0218202503002660

## ERROR ESTIMATES FOR A CLASS OF FINITE DIFFERENCE-QUADRATURE SCHEMES FOR FULLY NONLINEAR DEGENERATE PARABOLIC INTEGRO-PDES

IMRAN H. BISWAS, ESPEN R. JAKOBSEN and KENNETH H. KARLSEN
Journal of Hyperbolic Differential Equations 05 (01) 187 (2008)
DOI: 10.1142/S0219891608001416

## Asymptotic Control for a Class of Piecewise Deterministic Markov Processes Associated to Temperate Viruses

Dan Goreac
SIAM Journal on Control and Optimization 53 (4) 1860 (2015)
DOI: 10.1137/140998913

## A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models

Rama Cont and Ekaterina Voltchkova
SIAM Journal on Numerical Analysis 43 (4) 1596 (2005)
DOI: 10.1137/S0036142903436186

## A Penalty Method for the Numerical Solution of Hamilton–Jacobi–Bellman (HJB) Equations in Finance

J. H. Witte and C. Reisinger
SIAM Journal on Numerical Analysis 49 (1) 213 (2011)
DOI: 10.1137/100797606

## Recent Developments in Numerical Methods for Fully Nonlinear Second Order Partial Differential Equations

Xiaobing Feng, Roland Glowinski and Michael Neilan
SIAM Review 55 (2) 205 (2013)
DOI: 10.1137/110825960

## On quadratic approximations for Hamilton–Jacobi–Bellman equations

Yumiharu Nakano
Automatica 66 205 (2016)
DOI: 10.1016/j.automatica.2016.01.001

## Error estimation and adaptive discretization for the discrete stochastic Hamilton?Jacobi?Bellman equation

Lars Gr�ne
Numerische Mathematik 99 (1) 85 (2004)
DOI: 10.1007/s00211-004-0555-4

## Convergence of Implicit Schemes for Hamilton--Jacobi--Bellman Quasi-Variational Inequalities

SIAM Journal on Control and Optimization 56 (6) 3994 (2018)
DOI: 10.1137/18M1171965

## Convergence Rate of an Explicit Finite Difference Scheme for a Credit Rating Migration Problem

Yan Li, Zhengce Zhang and Bei Hu
SIAM Journal on Numerical Analysis 56 (4) 2430 (2018)
DOI: 10.1137/17M1151833

## Approximation schemes for viscosity solutions of fully nonlinear stochastic partial differential equations

Benjamin Seeger
The Annals of Applied Probability 30 (4) (2020)
DOI: 10.1214/19-AAP1543

## Error estimates for approximations of nonlinear uniformly parabolic equations

Olga Turanova
Nonlinear Differential Equations and Applications NoDEA 22 (3) 345 (2015)
DOI: 10.1007/s00030-014-0286-x

## Convergence Rate Estimates for Aleksandrov's Solution to the Monge--Ampère Equation

Haodi Chen, Genggeng Huang and Xu-Jia Wang
SIAM Journal on Numerical Analysis 57 (1) 173 (2019)
DOI: 10.1137/18M1197217

## Large-time behavior of unbounded solutions of viscous Hamilton-Jacobi equations in RN

Guy Barles, Alexander Quaas and Andrei Rodríguez-Paredes
Communications in Partial Differential Equations 46 (3) 547 (2021)
DOI: 10.1080/03605302.2020.1846561

## Viscosity Solutions for a System of Integro-PDEs and Connections to Optimal Switching and Control of Jump-Diffusion Processes

Imran H. Biswas, Espen R. Jakobsen and Kenneth H. Karlsen
Applied Mathematics and Optimization 62 (1) 47 (2010)
DOI: 10.1007/s00245-009-9095-8

## Splitting methods for Hamilton-Jacobi equations

Agnès Tourin
Numerical Methods for Partial Differential Equations 22 (2) 381 (2006)
DOI: 10.1002/num.20100

## Encyclopedia of Quantitative Finance

Espen R. Jakobsen
Encyclopedia of Quantitative Finance (2010)
DOI: 10.1002/9780470061602.eqf12010

## On the LP formulation in measure spaces of optimal control problems for jump-diffusions

Rafael Serrano
Systems & Control Letters 85 33 (2015)
DOI: 10.1016/j.sysconle.2015.08.008

## On the Rate of Convergence for Monotone Numerical Schemes for Nonlocal Isaacs Equations

Imran H. Biswas, Indranil Chowdhury and Espen R. Jakobsen
SIAM Journal on Numerical Analysis 57 (2) 799 (2019)
DOI: 10.1137/17M114995X

## Dynamic Interest-Rate Modelling in Incomplete Markets

Jesus Perez Colino
SSRN Electronic Journal (2008)
DOI: 10.2139/ssrn.2098419

## An Approximation Scheme for Semilinear Parabolic PDEs with Convex and Coercive Hamiltonians

Shuo Huang, Gechun Liang and Thaleia Zariphopoulou
SIAM Journal on Control and Optimization 58 (1) 165 (2020)
DOI: 10.1137/18M1198831

## Error Estimates of Penalty Schemes for Quasi-Variational Inequalities Arising from Impulse Control Problems

Christoph Reisinger and Yufei Zhang
SIAM Journal on Control and Optimization 58 (1) 243 (2020)
DOI: 10.1137/19M124040X

## On the structure of multifactor optimal portfolio strategies

Nikolai Dokuchaev
ESAIM: Control, Optimisation and Calculus of Variations 24 (3) 1043 (2018)
DOI: 10.1051/cocv/2017013

## Dynamic portfolio selection with nonlinear transaction costs

Thamayanthi Chellathurai and Thangaraj Draviam
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461 (2062) 3183 (2005)
DOI: 10.1098/rspa.2005.1518

## Qualitative properties of generalized principal eigenvalues for superquadratic viscous Hamilton–Jacobi equations

Emmanuel Chasseigne and Naoyuki Ichihara
Nonlinear Differential Equations and Applications NoDEA 23 (6) (2016)
DOI: 10.1007/s00030-016-0422-x

## Hamilton–Jacobi equations for optimal control on multidimensional junctions with entry costs

Manh-Khang Dao and Boualem Djehiche
Nonlinear Differential Equations and Applications NoDEA 27 (2) (2020)
DOI: 10.1007/s00030-020-0625-z

## Outperforming the market portfolio with a given probability

Erhan Bayraktar, Yu-Jui Huang and Qingshuo Song
The Annals of Applied Probability 22 (4) (2012)
DOI: 10.1214/11-AAP799

## Error estimation for second‐order partial differential equations in nonvariational form

Jan Blechschmidt, Roland Herzog and Max Winkler
Numerical Methods for Partial Differential Equations 37 (3) 2190 (2021)
DOI: 10.1002/num.22678

## Improved order 1/4 convergence for piecewise constant policy approximation of stochastic control problems

Espen R. Jakobsen, Athena Picarelli and Christoph Reisinger
Electronic Communications in Probability 24 (none) (2019)
DOI: 10.1214/19-ECP256
Q.S. Song and G. Yin
3108 (2007)
DOI: 10.1109/CDC.2007.4434198
Qingshuo Song and G. Yin
567 (2010)
DOI: 10.1109/CDC.2010.5717658

## Actor-Critic Method for High Dimensional Static Hamilton--Jacobi--Bellman Partial Differential Equations based on Neural Networks

Mo Zhou, Jiequn Han and Jianfeng Lu
SIAM Journal on Scientific Computing 43 (6) A4043 (2021)
DOI: 10.1137/21M1402303

## Discrete‐time approximation for stochastic optimal control problems under the G ‐expectation framework

Lianzi Jiang
Optimal Control Applications and Methods 43 (2) 418 (2022)
DOI: 10.1002/oca.2814

## Stochastic Target Games and Dynamic Programming via Regularized Viscosity Solutions

Bruno Bouchard and Marcel Nutz
Mathematics of Operations Research 41 (1) 109 (2016)
DOI: 10.1287/moor.2015.0718

## SIR Epidemics with State-Dependent Costs and ICU Constraints: A Hamilton–Jacobi Verification Argument and Dual LP Algorithms

Lorenzo Freddi, Dan Goreac, Juan Li and Boxiang Xu
Applied Mathematics & Optimization 86 (2) (2022)
DOI: 10.1007/s00245-022-09884-x

## On representation formulas for optimal control: A Lagrangian perspective

Yeoneung Kim and Insoon Yang
IET Control Theory & Applications 16 (16) 1633 (2022)
DOI: 10.1049/cth2.12329