{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:41:00Z","timestamp":1787323260672,"version":"build-2736575974"},"reference-count":51,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"8","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>This paper studies regularity properties of the value function for an infinite-horizon discounted cost impulse control problem, where the underlying controlled process is a multidimensional jump diffusion with possibly \u201cinfinite-activity\u201d jumps. Surprisingly, despite these jumps, we obtain the same degree of regularity as for the diffusion case, at least when the jump satisfies certain integrability conditions.<\/jats:p>","DOI":"10.1137\/090780419","type":"journal-article","created":{"date-parts":[[2010,11,5]],"date-time":"2010-11-05T20:13:40Z","timestamp":1288988020000},"page":"5276-5293","source":"Crossref","is-referenced-by-count":58,"title":["Impulse Control of Multidimensional Jump Diffusions"],"prefix":"10.1137","volume":"48","author":[{"given":"Mark H. A.","family":"Davis","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xin","family":"Guo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guoliang","family":"Wu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,11,4]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.anihpc.2007.02.007"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/080712519"},{"key":"R3","unstructured":"A. Bensoussan and J.L. Lions,\n                      Impulse control and quasivariational inequalities\n                      , Heyden & Son, Inc., Philadelphia, 1984. Translation of\n                      Contr\u00f4le Impulsionnel et In\u00e9quations Quasi-variationnelles\n                      , Gauthier-Villars, Paris, 1982."},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/s007800050001"},{"key":"R5","first-page":"333","volume":"265","author":"Bony J.-M.","year":"1967","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. A"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2008.07.007"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.2006.00267.x"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1006\/jeth.1999.2523"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9965.00020"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1287\/opre.26.4.620"},{"key":"R11","unstructured":"R. Cont and P. Tankov,\n                      Financial Modelling with Jump Processes\n                      , Chapman & Hall\/CRC, Boca Raton, FL, 2004."},{"key":"R12","doi-asserted-by":"crossref","unstructured":"M. G. Crandall,\n                      Viscosity solutions: A primer\n                      , in Viscosity Solutions and Applications (Montecatini Terme, 1995), Lecture Notes in Math. 1660, Springer, Berlin, 1997, pp. 1\u201343.","DOI":"10.1007\/BFb0094294"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"M. G. Crandall, H. Ishii, and P. L. Lions,\n                      User's guide to viscosity solutions of second order partial differential equations\n                      , Bull. Amer. Math. Soc. (N.S.) 27 (1992), pp. 1\u201367.","DOI":"10.1090\/S0273-0979-1992-00266-5"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1287\/moor.13.4.588"},{"key":"R15","doi-asserted-by":"crossref","unstructured":"E. Eberlein,\n                      Application of generalized hyperbolic L\u00e9vy motions to finance\n                      , in L\u00e9vy Processes, O. E. Barndorff-Nielsen, ed., Birkh\u00e4user Boston, Boston, 2001, pp. 319\u2013336.","DOI":"10.1007\/978-1-4612-0197-7_14"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"M. G. Garroni and J. L. Menaldi,\n                      Second Order Elliptic Integro-Differential Problems\n                      , Chapman & Hall\/CRC, Boca Raton, FL, 2002.","DOI":"10.1201\/9781420035797"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"I. I. Gihman and A. V. Skorohod,\n                      Controlled Stochastic Processes\n                      , translated from the Russian by Samuel Kotz, Springer-Verlag, New York, Heidelberg, 1979.","DOI":"10.1007\/978-1-4612-6202-2"},{"key":"R18","unstructured":"D. Gilbarg and N. S. Trudinger,\n                      Elliptic Partial Differential Equations of Second Order\n                      , Springer-Verlag, Berlin, 1998."},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/060669024"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1137\/080716001"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1287\/moor.8.3.454"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1287\/moor.8.3.439"},{"key":"R23","unstructured":"N. Ikeda and S. Watanabe,\n                      Stochastic Differential Equations and Diffusion Processes\n                      , 2nd ed., North\u2013Holland, Amsterdam, 1989."},{"key":"R24","first-page":"101","volume":"38","author":"Ishii H.","year":"1995","journal-title":"Funkcial. Ekvac.","ISSN":"https:\/\/id.crossref.org\/issn\/0532-8721","issn-type":"print"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-004-0795-9"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1070\/RM1995v050n02ABEH002054"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.1993.tb00085.x"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1007\/s001860000048"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1007\/s007800050034"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1007\/s001860050083"},{"key":"R31","unstructured":"O. A. Ladyzhenskaya and N. N. Ural'tseva,\n                      Linear and Quasilinear Elliptic Equations\n                      , translated from the Russian by Scripta Technica, Inc., L. Ehrenpreis, translation ed., Academic Press, New York, London, 1968."},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-008-0073-9"},{"key":"R33","doi-asserted-by":"crossref","unstructured":"G. M. Lieberman,\n                      Second Order Parabolic Differential Equations\n                      , World Scientific, River Edge, NJ, 1996.","DOI":"10.1142\/3302"},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1983-0699422-3"},{"key":"R35","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-006-0025-1"},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.1137\/0330053"},{"key":"R37","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1994.tb02453.x"},{"key":"R38","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.1995.tb00071.x"},{"key":"R39","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4068(97)00013-X"},{"key":"R40","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012900376013"},{"key":"R41","unstructured":"B. \u00d8ksendal and A. Sulem,\n                      Applied Stochastic Control of Jump Diffusions\n                      , Universitext, Springer-Verlag, Berlin, 2004."},{"key":"R42","doi-asserted-by":"publisher","DOI":"10.1007\/s002459900042"},{"key":"R43","doi-asserted-by":"crossref","unstructured":"H. Pham,\n                      On the smooth-fit property for one-dimensional optimal switching problem\n                      , in S\u00e9minaire de Probabilit\u00e9s XL, Lecture Notes in Math. 189, Springer, New York, 2007, pp. 187\u2013199.","DOI":"10.1007\/978-3-540-71189-6_8"},{"key":"R44","unstructured":"R. C. Seydel,\n                      General existence and uniqueness of viscosity solutions for impulse control of jump-diffusions\n                      , MPI MIS Preprint 37\/2008, Leipzig, Germany, 2008."},{"key":"R45","doi-asserted-by":"crossref","unstructured":"R. C. Seydel,\n                      Existence and uniqueness of viscosity solutions for QVI associated with impulse control of jump-diffusions\n                      , Stochastic Process. Appl., 2009, pp. 3719\u20133748.","DOI":"10.1016\/j.spa.2009.07.004"},{"key":"R46","doi-asserted-by":"publisher","DOI":"10.1137\/0324067"},{"key":"R47","doi-asserted-by":"publisher","DOI":"10.1287\/moor.10.1.63"},{"key":"R48","doi-asserted-by":"publisher","DOI":"10.1080\/17442509308833860"},{"key":"R49","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1990.tb03702.x"},{"key":"R50","doi-asserted-by":"publisher","DOI":"10.1017\/S0956792505006340"},{"key":"R51","unstructured":"J. M. Yong and X. Y. Zhou,\n                      Stochastic Controls: Hamiltonian Systems and HJB Equations\n                      , Springer-Verlag, New York, 1999."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/090780419","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:51:32Z","timestamp":1787320292000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/090780419"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":51,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/090780419"],"URL":"https:\/\/doi.org\/10.1137\/090780419","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}