{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T11:49:39Z","timestamp":1759664979089},"reference-count":32,"publisher":"Cambridge University Press (CUP)","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2012,3]]},"abstract":"<jats:p>In the last few years there has been renewed interest in the classical control problem of de Finetti (1957) for the case where the underlying source of randomness is a spectrally negative L\u00e9vy process. In particular, a significant step forward was made by Loeffen (2008), who showed that a natural and very general condition on the underlying L\u00e9vy process which allows one to proceed with the analysis of the associated Hamilton-Jacobi-Bellman equation is that its L\u00e9vy measure is absolutely continuous, having completely monotone density. In this paper we consider de Finetti's control problem, but with the restriction that control strategies are absolutely continuous with respect to the Lebesgue measure. This problem has been considered by Asmussen and Taksar (1997), Jeanblanc-Picqu\u00e9 and Shiryaev (1995), and Boguslavskaya (2006) in the diffusive case, and Gerber and Shiu (2006) for the case of a Cram\u00e9r-Lundberg process with exponentially distributed jumps. We show the robustness of the condition that the underlying L\u00e9vy measure has a completely monotone density and establish an explicit optimal strategy for this case that envelopes the aforementioned existing results. The explicit optimal strategy in question is the so-called refraction strategy.<\/jats:p>","DOI":"10.1017\/s0021900200008913","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T14:50:26Z","timestamp":1459263026000},"page":"150-166","source":"Crossref","is-referenced-by-count":7,"title":["Optimal Control with Absolutely Continuous Strategies for Spectrally Negative L\u00e9vy Processes"],"prefix":"10.1017","volume":"49","author":[{"given":"Andreas E.","family":"Kyprianou","sequence":"first","affiliation":[]},{"given":"Ronnie","family":"Loeffen","sequence":"additional","affiliation":[]},{"given":"Jos\u00e9-Luis","family":"P\u00e9rez","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,2,4]]},"reference":[{"key":"S0021900200008913_ref33","volume-title":"Probability with Martingales","year":"1991"},{"key":"S0021900200008913_ref21","volume-title":"Introductory Lectures on Fluctuations of L\u00e9vy Processes with Applications","year":"2006"},{"key":"S0021900200008913_ref31","volume-title":"Stochastic Control in Insurance","year":"2008"},{"key":"S0021900200008913_ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2009.09.006"},{"key":"S0021900200008913_ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2009.03.002"},{"key":"S0021900200008913_ref26","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1238592118"},{"key":"S0021900200008913_ref25","doi-asserted-by":"publisher","DOI":"10.1214\/07-AAP504"},{"key":"S0021900200008913_ref24","doi-asserted-by":"publisher","DOI":"10.1007\/s10959-009-0220-z"},{"key":"S0021900200008913_ref23","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1183667406"},{"key":"S0021900200008913_ref22","doi-asserted-by":"publisher","DOI":"10.1214\/08-AIHP307"},{"key":"S0021900200008913_ref20","doi-asserted-by":"publisher","DOI":"10.1214\/105051604000000927"},{"key":"S0021900200008913_ref30","first-page":"1373","volume-title":"J. 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