caa a22 4500 445842296 CHVBK 20180317145348.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00245-010-9122-9 doi (NATIONALLICENCE)springer-10.1007/s00245-010-9122-9 Convex Hamilton-Jacobi Equations Under Superlinear Growth Conditions on Data [Elektronische Daten] [Francesca Da Lio, Olivier Ley] Unbounded stochastic control problems may lead to Hamilton-Jacobi-Bellman equations whose Hamiltonians are not always defined, especially when the diffusion term is unbounded with respect to the control. We obtain existence and uniqueness of viscosity solutions growing at most like o(1+|x|p) at infinity for such HJB equations and more generally for degenerate parabolic equations with a superlinear convex gradient nonlinearity. If the corresponding control problem has a bounded diffusion with respect to the control, then our results apply to a larger class of solutions, namely those growing like O(1+|x|p) at infinity. This latter case encompasses some equations related to backward stochastic differential equations. Springer Science+Business Media, LLC, 2010 Degenerate parabolic equations nationallicence Hamilton-Jacobi-Bellman equations nationallicence Viscosity solutions nationallicence Unbounded solutions nationallicence Maximum principle nationallicence Backward stochastic differential equations nationallicence Unbounded stochastic control problems nationallicence Da Lio Francesca Dipartimento di Matematica Pura e Applicata, Via Trieste, 63, 35121, Padova, Italy aut Ley Olivier IRMAR, INSA de Rennes, 35708, Rennes, France aut Applied Mathematics & Optimization Springer-Verlag 63/3(2011-06-01), 309-339 0095-4616 63:3<309 2011 63 245 https://doi.org/10.1007/s00245-010-9122-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00245-010-9122-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Da Lio Francesca Dipartimento di Matematica Pura e Applicata, Via Trieste, 63, 35121, Padova, Italy aut NATIONALLICENCE 700 1- Ley Olivier IRMAR, INSA de Rennes, 35708, Rennes, France aut NATIONALLICENCE 773 0- Applied Mathematics & Optimization Springer-Verlag 63/3(2011-06-01), 309-339 0095-4616 63:3<309 2011 63 245 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer