{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T02:18:07Z","timestamp":1743041887849,"version":"3.40.3"},"publisher-location":"London","reference-count":35,"publisher":"Springer London","isbn-type":[{"type":"electronic","value":"9781447151029"}],"license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-1-4471-5102-9_232-1","type":"book-chapter","created":{"date-parts":[[2014,5,16]],"date-time":"2014-05-16T19:28:05Z","timestamp":1400268485000},"page":"1-7","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Numerical Methods for Continuous-Time Stochastic Control Problems"],"prefix":"10.1007","author":[{"given":"George","family":"Yin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,3,31]]},"reference":[{"key":"232-1_CR1","first-page":"271","volume":"4","author":"G Barles","year":"1991","unstructured":"Barles G, Souganidis P (1991) Convergence of approximation schemes for fully nonlinear second order equations. J Asymptot Anal 4:271\u2013283","journal-title":"J Asymptot Anal"},{"key":"232-1_CR2","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1109\/9.24227","volume":"34","author":"DP Bertsekas","year":"1989","unstructured":"Bertsekas DP, Castanon DA (1989) Adaptive aggregation methods for infinite horizon dynamic programming. IEEE Trans Autom Control 34:589\u2013598","journal-title":"IEEE Trans Autom Control"},{"key":"232-1_CR3","volume-title":"An expert system for control and signal processing with automatic FORTRAN program generation","author":"P Chancelier","year":"1986","unstructured":"Chancelier P, Gomez C, Quadrat J-P, Sulem A, Blankenship GL, La Vigna A, MaCenary DC, Yan\u00a0I (1986) An expert system for control and signal processing with automatic FORTRAN program generation. In: Mathematical systems symposium, Stockholm. Royal Institute of Technology, Stockholm"},{"key":"232-1_CR4","volume-title":"IMA volume in mathematics and its applications, vol 10","author":"P Chancelier","year":"1987","unstructured":"Chancelier P, Gomez C, Quadrat J-P, Sulem A (1987) Automatic study in stochastic control. In: Fleming W, Lions PL (eds) IMA volume in mathematics and its applications, vol 10. Springer, Berlin"},{"key":"232-1_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1090\/S0002-9947-1983-0690039-8","volume":"277","author":"MG Crandall","year":"1983","unstructured":"Crandall MG, Lions PL (1983) Viscosity solutions of Hamilton-Jacobi equations. Trans Am Math Soc 277:1\u201342","journal-title":"Trans Am Math Soc"},{"key":"232-1_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1090\/S0273-0979-1992-00266-5","volume":"27","author":"MG Crandall","year":"1992","unstructured":"Crandall MG, Ishii H, Lions PL (1992) User\u2019s guide to viscosity solutions of second order partial differential equations. Bull Am Math Soc 27:1\u201367","journal-title":"Bull Am Math Soc"},{"key":"232-1_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6380-7","volume-title":"Deterministic and stochastic optimal control","author":"WH Fleming","year":"1975","unstructured":"Fleming WH, Rishel RW (1975) Deterministic and stochastic optimal control. Springer, New York"},{"key":"232-1_CR8","volume-title":"Controlled Markov processes and viscosity solutions","author":"WH Fleming","year":"1992","unstructured":"Fleming WH, Soner HM (1992) Controlled Markov processes and viscosity solutions. Springer, New York"},{"key":"232-1_CR9","doi-asserted-by":"publisher","first-page":"2842","DOI":"10.1016\/j.cam.2010.12.003","volume":"235","author":"Z Jin","year":"2011","unstructured":"Jin Z, Wang Y, Yin G (2011) Numerical solutions of quantile hedging for guaranteed minimum death benefits under a regime-switching-jump-diffusion formulation. J Comput Appl Math 235:2842\u20132860","journal-title":"J Comput Appl Math"},{"key":"232-1_CR10","doi-asserted-by":"publisher","first-page":"1489","DOI":"10.1016\/j.automatica.2012.05.039","volume":"48","author":"Z Jin","year":"2012","unstructured":"Jin Z, Yin G, Zhu C (2012) Numerical solutions of optimal risk control and dividend optimization policies under a generalized singular control formulation. Automatica 48:1489\u20131501","journal-title":"Automatica"},{"key":"232-1_CR11","doi-asserted-by":"publisher","first-page":"2317","DOI":"10.1016\/j.automatica.2013.04.043","volume":"49","author":"Z Jin","year":"2013","unstructured":"Jin Z, Yang HL, Yin G (2013) Numerical methods for optimal dividend payment and investment strategies of regime-switching jump diffusion models with capital injections. Automatica 49:2317\u20132329","journal-title":"Automatica"},{"key":"232-1_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s004400050264","volume":"117","author":"VN Krylov","year":"2000","unstructured":"Krylov VN (2000) On the rate of convergence of finite-difference approximations for Bellman\u2019s equations with variable coefficients. Probab Theory Relat Fields 117:1\u201316","journal-title":"Probab Theory Relat Fields"},{"key":"232-1_CR13","volume-title":"Probability methods for approximation in stochastic control and for elliptic equations","author":"HJ Kushner","year":"1977","unstructured":"Kushner HJ (1977) Probability methods for approximation in stochastic control and for elliptic equations. Academic, New York"},{"key":"232-1_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4482-0","volume-title":"Weak convergence methods and singularly perturbed stochastic control and filtering problems","author":"HJ Kushner","year":"1990","unstructured":"Kushner HJ (1990a) Weak convergence methods and singularly perturbed stochastic control and filtering problems. Birkh\u00e4user, Boston"},{"key":"232-1_CR15","doi-asserted-by":"publisher","first-page":"999","DOI":"10.1137\/0328056","volume":"28","author":"HJ Kushner","year":"1990","unstructured":"Kushner HJ (1990b) Numiercal methods for stochastic control problems in continuous time. SIAM J Control Optim 28:999\u20131048","journal-title":"SIAM J Control Optim"},{"key":"232-1_CR16","doi-asserted-by":"publisher","first-page":"2283","DOI":"10.1109\/9.811211","volume":"44","author":"HJ Kushner","year":"2000","unstructured":"Kushner HJ (2000) Consistency issues for numerical methods for variance control with applications to optimization in finance. IEEE Trans Autom Control 44:2283\u20132296","journal-title":"IEEE Trans Autom Control"},{"key":"232-1_CR17","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1137\/S0363012901389457","volume":"40","author":"HJ Kushner","year":"2002","unstructured":"Kushner HJ (2002) Numerical approximations for stochastic differential games. SIAM J Control Optim 40:457\u2013486","journal-title":"SIAM J Control Optim"},{"key":"232-1_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-4621-9","volume-title":"Numerical methods for controlled stochastic delay systems","author":"HJ Kushner","year":"2008","unstructured":"Kushner HJ (2008) Numerical methods for controlled stochastic delay systems. Birkh\u00e4user, Boston"},{"key":"232-1_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-0441-8","volume-title":"Numerical methods for stochastic control problems in continuous time","author":"HJ Kushner","year":"1992","unstructured":"Kushner HJ, Dupuis PG (1992) Numerical methods for stochastic control problems in continuous time. Springer, New York"},{"key":"232-1_CR20","doi-asserted-by":"publisher","first-page":"344","DOI":"10.1109\/TAC.1968.1098939","volume":"AC-13","author":"HJ Kushner","year":"1968","unstructured":"Kushner HJ, Kleinman AJ (1968) Numerical methods for the solution of the degenerate nonlinear elliptic equations arising in optimal stochastic control theory. IEEE Trans Autom Control AC-13:344\u2013353","journal-title":"IEEE Trans Autom Control"},{"key":"232-1_CR21","volume-title":"Stochastic approximation and recursive algorithms and applications","author":"HJ Kushner","year":"2003","unstructured":"Kushner HJ, Yin G (2003) Stochastic approximation and recursive algorithms and applications, 2nd edn. Springer, New York","edition":"2"},{"key":"232-1_CR22","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1137\/0327031","volume":"27","author":"J Menaldi","year":"1989","unstructured":"Menaldi J (1989) Some estimates for finite difference approximations. SIAM J Control Optim 27:579\u2013607","journal-title":"SIAM J Control Optim"},{"key":"232-1_CR23","doi-asserted-by":"publisher","first-page":"966","DOI":"10.1137\/0328054","volume":"28","author":"S Peng","year":"1990","unstructured":"Peng S (1990) A general stochastic maximum principle for optimal control problems. SIAM J Control Optim 28:966\u2013979","journal-title":"SIAM J Control Optim"},{"key":"232-1_CR24","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0285-1","volume-title":"Hierarchical decision making in stochastic manufacturing systems","author":"SP Sethi","year":"1994","unstructured":"Sethi SP, Zhang Q (1994) Hierarchical decision making in stochastic manufacturing systems. Birkh\u00e4user, Boston"},{"key":"232-1_CR25","doi-asserted-by":"publisher","first-page":"1831","DOI":"10.1137\/070679843","volume":"48","author":"QS Song","year":"2009","unstructured":"Song QS, Yin G (2009) Rates of convergence of numerical methods for controlled regime-switching diffusions with stopping times in the costs. SIAM J Control Optim 48:1831\u20131857","journal-title":"SIAM J Control Optim"},{"key":"232-1_CR26","doi-asserted-by":"publisher","first-page":"1147","DOI":"10.1016\/j.automatica.2006.03.016","volume":"42","author":"QS Song","year":"2006","unstructured":"Song QS, Yin G, Zhang Z (2006) Numerical method for controlled regime-switching diffusions and regime-switching jump diffusions. Automatica 42:1147\u20131157","journal-title":"Automatica"},{"key":"232-1_CR27","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1109\/TAC.2007.915169","volume":"53","author":"QS Song","year":"2008","unstructured":"Song QS, Yin G, Zhang Z (2008) Numerical solutions for stochastic differential games with regime switching. IEEE Trans Autom Control 53:509\u2013521","journal-title":"IEEE Trans Autom Control"},{"key":"232-1_CR28","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1016\/0022-247X(62)90033-1","volume":"4","author":"J Warga","year":"1962","unstructured":"Warga J (1962) Relaxed variational problems. J Math Anal Appl 4:111\u2013128","journal-title":"J Math Anal Appl"},{"key":"232-1_CR29","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1007\/BF02207640","volume":"83","author":"HM Yan","year":"1994","unstructured":"Yan HM, Yin G, Lou SXC (1994) Using stochastic optimization to determine threshold values for control of unreliable manufacturing systems. J Optim Theory Appl 83:511\u2013539","journal-title":"J Optim Theory Appl"},{"key":"232-1_CR30","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-4346-9","volume-title":"Continuous-time Markov chains and applications: a two-time-scale approach","author":"G Yin","year":"2013","unstructured":"Yin G, Zhang Q (2013) Continuous-time Markov chains and applications: a two-time-scale approach, 2nd edn. Springer, New York","edition":"2"},{"key":"232-1_CR31","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-1105-6","volume-title":"Hybrid switching diffusions: properties and applications","author":"G Yin","year":"2010","unstructured":"Yin G, Zhu C (2010) Hybrid switching diffusions: properties and applications. Springer, New York"},{"key":"232-1_CR32","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1137\/S1052623401392901","volume":"13","author":"G Yin","year":"2002","unstructured":"Yin G, Liu RH, Zhang Q (2002) Recursive algorithms for stock liquidation: a stochastic optimization approach. SIAM J Optim 13:240\u2013263","journal-title":"SIAM J Optim"},{"key":"232-1_CR33","doi-asserted-by":"publisher","first-page":"564","DOI":"10.1016\/j.cam.2009.08.055","volume":"233","author":"G Yin","year":"2009","unstructured":"Yin G, Jin H, Jin Z (2009) Numerical methods for portfolio selection with bounded constraints. J Comput Appl Math 233:564\u2013581","journal-title":"J Comput Appl Math"},{"key":"232-1_CR34","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1466-3","volume-title":"Stochastic controls: Hamiltonian systems and HJB equations","author":"J Yong","year":"1999","unstructured":"Yong J, Zhou XY (1999) Stochastic controls: Hamiltonian systems and HJB equations. Springer, New York"},{"key":"232-1_CR35","doi-asserted-by":"publisher","first-page":"1755","DOI":"10.1090\/S0025-5718-06-01876-X","volume":"75","author":"J Zhang","year":"2006","unstructured":"Zhang J (2006) Rate of convergence of finite difference approximations for degenerate ODEs. Math Comput 75:1755\u20131778","journal-title":"Math Comput"}],"container-title":["Encyclopedia of Systems and Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-1-4471-5102-9_232-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T04:50:35Z","timestamp":1676868635000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-1-4471-5102-9_232-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9781447151029"],"references-count":35,"URL":"https:\/\/doi.org\/10.1007\/978-1-4471-5102-9_232-1","relation":{},"subject":[],"published":{"date-parts":[[2014]]},"assertion":[{"value":"3 March 2014, 01:34:29","order":1,"name":"received","label":"Received","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"3 March 2014, 01:34:29","order":2,"name":"accepted","label":"Accepted","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"31 March 2014","order":3,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}