Lee, Junbeom; Yu, Xiang; Zhou, Chao Lifetime ruin under high-water mark fees and drift uncertainty. (English) Zbl 1471.91503 Appl. Math. Optim. 84, No. 3, 2743-2773 (2021). MSC: 91G10 49L25 PDFBibTeX XMLCite \textit{J. Lee} et al., Appl. Math. Optim. 84, No. 3, 2743--2773 (2021; Zbl 1471.91503) Full Text: DOI arXiv
Picarelli, Athena; Reisinger, Christoph; Rotaetxe Arto, Julen Some regularity and convergence results for parabolic Hamilton-Jacobi-Bellman equations in bounded domains. (English) Zbl 1439.35292 J. Differ. Equations 268, No. 12, 7843-7876 (2020). MSC: 35K61 49L25 65M15 65M06 93E20 PDFBibTeX XMLCite \textit{A. Picarelli} et al., J. Differ. Equations 268, No. 12, 7843--7876 (2020; Zbl 1439.35292) Full Text: DOI arXiv
Bayraktar, Erhan; Li, Jiaqi On the controller-stopper problems with controlled jumps. (English) Zbl 1422.91081 Appl. Math. Optim. 80, No. 1, 195-222 (2019). MSC: 91A15 91A55 91A12 49L25 60G40 PDFBibTeX XMLCite \textit{E. Bayraktar} and \textit{J. Li}, Appl. Math. Optim. 80, No. 1, 195--222 (2019; Zbl 1422.91081) Full Text: DOI arXiv
Guasoni, Paolo; Huang, Yu-Jui Consumption, investment and healthcare with aging. (English) Zbl 1411.91365 Finance Stoch. 23, No. 2, 313-358 (2019). MSC: 91B42 93E20 49L25 PDFBibTeX XMLCite \textit{P. Guasoni} and \textit{Y.-J. Huang}, Finance Stoch. 23, No. 2, 313--358 (2019; Zbl 1411.91365) Full Text: DOI arXiv
Hamadène, Said; Zhao, Xuzhe Viscosity solutions of systems of variational inequalities with interconnected bilateral obstacles of non-local type. (English) Zbl 1406.49041 J. Dyn. Differ. Equations 30, No. 4, 1731-1756 (2018). Reviewer: Zhang Xian (Xiamen) MSC: 49N70 93E20 60H10 49J40 49L25 90C39 49J35 PDFBibTeX XMLCite \textit{S. Hamadène} and \textit{X. Zhao}, J. Dyn. Differ. Equations 30, No. 4, 1731--1756 (2018; Zbl 1406.49041) Full Text: DOI arXiv
Hernández-Hernández, Daniel; Sîrbu, Mihai Zero-sum stochastic differential games without the Isaacs condition: random rules of priority and intermediate Hamiltonians. (English) Zbl 1391.91028 SIAM J. Control Optim. 56, No. 3, 2095-2119 (2018). MSC: 91A15 91A05 49L25 PDFBibTeX XMLCite \textit{D. Hernández-Hernández} and \textit{M. Sîrbu}, SIAM J. Control Optim. 56, No. 3, 2095--2119 (2018; Zbl 1391.91028) Full Text: DOI arXiv
Bayraktar, Erhan; Li, Jiaqi Stochastic Perron for stochastic target problems. (English) Zbl 1346.93394 J. Optim. Theory Appl. 170, No. 3, 1026-1054 (2016). MSC: 93E20 49L20 49L25 60G46 PDFBibTeX XMLCite \textit{E. Bayraktar} and \textit{J. Li}, J. Optim. Theory Appl. 170, No. 3, 1026--1054 (2016; Zbl 1346.93394) Full Text: DOI arXiv Link
Bayraktar, Erhan; Zhang, Yuchong Minimizing the probability of lifetime ruin under ambiguity aversion. (English) Zbl 1343.49028 SIAM J. Control Optim. 53, No. 1, 58-90 (2015). MSC: 49J55 49L25 49L20 93E20 60H30 60G46 91B30 35Q93 35D40 PDFBibTeX XMLCite \textit{E. Bayraktar} and \textit{Y. Zhang}, SIAM J. Control Optim. 53, No. 1, 58--90 (2015; Zbl 1343.49028) Full Text: DOI arXiv
Djehiche, Boualem; Hamadène, Said; Morlais, Marie-Amelie Viscosity solutions of systems of variational inequalities with interconnected bilateral obstacles. (English) Zbl 1325.49014 Funkc. Ekvacioj, Ser. Int. 58, No. 1, 135-175 (2015). MSC: 49J40 49N70 49L25 60H10 60H30 90C39 93E20 PDFBibTeX XMLCite \textit{B. Djehiche} et al., Funkc. Ekvacioj, Ser. Int. 58, No. 1, 135--175 (2015; Zbl 1325.49014) Full Text: DOI arXiv
Sîrbu, Mihai Asymptotic Perron’s method and simple Markov strategies in stochastic games and control. (English) Zbl 1336.91017 SIAM J. Control Optim. 53, No. 4, 1713-1733 (2015). Reviewer: Vivek S. Borkar (Mumbai) MSC: 91A15 91A23 91A05 49L25 49L20 PDFBibTeX XMLCite \textit{M. Sîrbu}, SIAM J. Control Optim. 53, No. 4, 1713--1733 (2015; Zbl 1336.91017) Full Text: DOI arXiv
Salsa, Sandro Partial differential equations in action. From modelling to theory. 2nd ed. (English) Zbl 1320.35001 Unitext 86. La Matematica per il 3+2. Cham: Springer (ISBN 978-3-319-15092-5/pbk; 978-3-319-15093-2/ebook). xviii, 688 p. (2015). Reviewer: Dian K. Palagachev (Bari) MSC: 35-01 46-01 35L65 46E35 49K20 PDFBibTeX XMLCite \textit{S. Salsa}, Partial differential equations in action. From modelling to theory. 2nd ed. Cham: Springer (2015; Zbl 1320.35001) Full Text: DOI
Sîrbu, Mihai A note on the strong formulation of stochastic control problems with model uncertainty. (English) Zbl 1325.49025 Electron. Commun. Probab. 19, Paper No. 81, 10 p. (2014). MSC: 49J55 93E20 91A15 91A05 49L20 49L25 PDFBibTeX XMLCite \textit{M. Sîrbu}, Electron. Commun. Probab. 19, Paper No. 81, 10 p. (2014; Zbl 1325.49025) Full Text: DOI arXiv
Rokhlin, Dmitry B. Stochastic Perron’s method for optimal control problems with state constraints. (English) Zbl 1310.93085 Electron. Commun. Probab. 19, Paper No. 73, 15 p. (2014). MSC: 93E20 49L25 60H30 PDFBibTeX XMLCite \textit{D. B. Rokhlin}, Electron. Commun. Probab. 19, Paper No. 73, 15 p. (2014; Zbl 1310.93085) Full Text: DOI arXiv
Sîrbu, Mihai Stochastic Perron’s method and elementary strategies for zero-sum differential games. (English) Zbl 1409.91029 SIAM J. Control Optim. 52, No. 3, 1693-1711 (2014). MSC: 91A15 91A23 91A05 49L25 PDFBibTeX XMLCite \textit{M. Sîrbu}, SIAM J. Control Optim. 52, No. 3, 1693--1711 (2014; Zbl 1409.91029) Full Text: DOI arXiv
Bayraktar, Erhan; Sîrbu, Mihai Stochastic Perron’s method for Hamilton-Jacobi-Bellman equations. (English) Zbl 1285.49019 SIAM J. Control Optim. 51, No. 6, 4274-4294 (2013). MSC: 49L25 49L20 49J55 60G46 60H30 35Q93 35D40 93E20 PDFBibTeX XMLCite \textit{E. Bayraktar} and \textit{M. Sîrbu}, SIAM J. Control Optim. 51, No. 6, 4274--4294 (2013; Zbl 1285.49019) Full Text: DOI arXiv
Barles, Guy An introduction to the theory of viscosity solutions for first-order Hamilton-Jacobi equations and applications. (English) Zbl 1269.49043 Loreti, Paola (ed.) et al., Hamilton-Jacobi equations: approximations, numerical analysis and applications. Based on the lectures of the CIME summer school, Cetraro, Italy, August 29–September 3, 2011. Berlin: Springer; Florence: Fondazione CIME (ISBN 978-3-642-36432-7/pbk; 978-3-642-36433-4/ebook). Lecture Notes in Mathematics 2074. CIME Foundation Subseries, 49-109 (2013). MSC: 49L25 PDFBibTeX XMLCite \textit{G. Barles}, Lect. Notes Math. 2074, 49--109 (2013; Zbl 1269.49043) Full Text: DOI
Soravia, Pierpaolo Existence of absolute minimizers for noncoercive Hamiltonians and viscosity solutions of the Aronsson equation. (English) Zbl 1264.35097 Math. Control Relat. Fields 2, No. 4, 399-427 (2012). MSC: 35D40 35J70 35J20 49J10 49N90 PDFBibTeX XMLCite \textit{P. Soravia}, Math. Control Relat. Fields 2, No. 4, 399--427 (2012; Zbl 1264.35097) Full Text: DOI
Kelome, Djivede; Święch, Andrzej Perron’s method and the method of relaxed limits for “unbounded” PDE in Hilbert spaces. (English) Zbl 1110.49027 Stud. Math. 176, No. 3, 249-277 (2006). MSC: 49L25 35R15 35J60 49L20 PDFBibTeX XMLCite \textit{D. Kelome} and \textit{A. Święch}, Stud. Math. 176, No. 3, 249--277 (2006; Zbl 1110.49027) Full Text: DOI
Koike, Shigeaki Perron’s method for \(L^p\)-viscosity solutions. (English) Zbl 1138.49025 Saitama Math. J. 23, 9-28 (2005). MSC: 49L25 35J60 35D05 35D10 49K20 PDFBibTeX XMLCite \textit{S. Koike}, Saitama Math. J. 23, 9--28 (2005; Zbl 1138.49025)
Barles, Guy; Da Lio, Francesca Remarks on the Dirichlet and state-constraint problems for quasilinear parabolic equations. (English) Zbl 1073.35120 Adv. Differ. Equ. 8, No. 8, 897-922 (2003). Reviewer: Jorge Ferreira (São João del-Rei) MSC: 35K60 35K55 35B05 35B50 49L25 PDFBibTeX XMLCite \textit{G. Barles} and \textit{F. Da Lio}, Adv. Differ. Equ. 8, No. 8, 897--922 (2003; Zbl 1073.35120)
Andrews, Ben; Feldman, Mikhail Nonlocal geometric expansion of convex planar curves. (English) Zbl 1029.49038 J. Differ. Equations 182, No. 2, 298-343 (2002). Reviewer: Hector O.Fattorini (Los Angeles) MSC: 49Q20 35G25 35K15 PDFBibTeX XMLCite \textit{B. Andrews} and \textit{M. Feldman}, J. Differ. Equations 182, No. 2, 298--343 (2002; Zbl 1029.49038) Full Text: DOI
Liu, Weian; Chen, Hua Viscosity solutions of nonlinear systems of degenerated elliptic equations of second order. (English) Zbl 0976.35019 Z. Anal. Anwend. 19, No. 4, 927-951 (2000). MSC: 35J55 35J70 49L25 35A05 35B65 PDFBibTeX XMLCite \textit{W. Liu} and \textit{H. Chen}, Z. Anal. Anwend. 19, No. 4, 927--951 (2000; Zbl 0976.35019) Full Text: DOI EuDML
Liu, Weian On the viscosity solutions for nonlinear systems of second order elliptic equations. (English) Zbl 0899.35038 Adv. Math., Beijing 26, No. 5, 474-476 (1997). MSC: 35J65 49L25 35J70 PDFBibTeX XMLCite \textit{W. Liu}, Adv. Math., Beijing 26, No. 5, 474--476 (1997; Zbl 0899.35038)
Crandall, Michael G. Viscosity solutions: A primer. (English) Zbl 0901.49026 Capuzzo Dolcetta, I. (ed.) et al., Viscosity solutions and applications. Lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (CIME), Montecatini Terme, Italy, June 12-20, 1995. Berlin: Springer. Lect. Notes Math. 1660, 1-43 (1997). Reviewer: P.Cannarsa (Roma) MSC: 49L25 35J70 35J60 49L20 35B05 49-01 PDFBibTeX XMLCite \textit{M. G. Crandall}, Lect. Notes Math. 1660, 1--43 (1997; Zbl 0901.49026)
Yamada, Naoki Viscosity solutions for integro-differential equations of Volterra type. (English) Zbl 0861.45009 Kenmochi, N. (ed.) et al., Proceedings of the Banach Center minisemester on nonlinear analysis and applications, Warsaw, Poland, November 14 – December 15, 1994. Tokyo: Gakkōtosho Co., Ltd. GAKUTO Int. Ser., Math. Sci. Appl. 7, 441-446 (1995). MSC: 45K05 49J22 45M05 PDFBibTeX XMLCite \textit{N. Yamada}, GAKUTO Int. Ser., Math. Sci. Appl. 7, 441--446 (1995; Zbl 0861.45009)
Ishii, Hitoshi Viscosity solutions of nonlinear partial differential equations. (English. Japanese original) Zbl 0968.35002 Sugaku Expo. 9, No. 2, 135-152 (1996); translation from Sugaku 46, No. 2, 144-157 (1994). MSC: 35-02 49L25 35D05 35B27 PDFBibTeX XML
Díaz, G.; Letelier, R. Uniqueness for viscosity solutions of quasilinear elliptic equations in \(\mathbb{R}{}^ N\) without conditions at infinity. (English) Zbl 0761.35020 Differ. Integral Equ. 5, No. 5, 999-1016 (1992). Reviewer: G.Hetzer (Auburn) MSC: 35J15 35D05 49L25 35B40 35B50 PDFBibTeX XMLCite \textit{G. Díaz} and \textit{R. Letelier}, Differ. Integral Equ. 5, No. 5, 999--1016 (1992; Zbl 0761.35020)
Crandall, Michael G.; Ishii, Hitoshi; Lions, Pierre-Louis User’s guide to viscosity solutions of second order partial differential equations. (English) Zbl 0755.35015 Bull. Am. Math. Soc., New Ser. 27, No. 1, 1-67 (1992). MSC: 35D05 35J60 35K55 35B05 35B50 35B25 35K65 35F20 49L25 35J25 35K20 35K15 PDFBibTeX XMLCite \textit{M. G. Crandall} et al., Bull. Am. Math. Soc., New Ser. 27, No. 1, 1--67 (1992; Zbl 0755.35015) Full Text: DOI arXiv Backlinks: MO
Lenhart, Suzanne M.; Yamada, Naoki Perron’s method for viscosity solutions associated with piecewise- deterministic processes. (English) Zbl 0731.45013 Funkc. Ekvacioj, Ser. Int. 34, No. 1, 173-186 (1991). Reviewer: P.Achuthan (Madras) MSC: 45K05 45G10 90C39 49L20 PDFBibTeX XMLCite \textit{S. M. Lenhart} and \textit{N. Yamada}, Funkc. Ekvacioj, Ser. Int. 34, No. 1, 173--186 (1991; Zbl 0731.45013)