{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T19:44:35Z","timestamp":1781120675903,"version":"3.54.1"},"reference-count":45,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2021,7,13]],"date-time":"2021-07-13T00:00:00Z","timestamp":1626134400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2022,10]]},"abstract":"<jats:p>This article concerns the tail probabilities of a light-tailed Markov-modulated L\u00e9vy process stopped at a state-dependent Poisson rate. The tails are shown to decay exponentially at rates given by the unique positive and negative roots of the spectral abscissa of a certain matrix-valued function. We illustrate the use of our results with an application to the stationary distribution of wealth in a simple economic model in which agents with constant absolute risk aversion are subject to random mortality and income fluctuation.<\/jats:p>","DOI":"10.1017\/s0266466621000268","type":"journal-article","created":{"date-parts":[[2021,7,13]],"date-time":"2021-07-13T03:28:41Z","timestamp":1626146921000},"page":"986-1013","source":"Crossref","is-referenced-by-count":11,"title":["TAIL BEHAVIOR OF STOPPED L\u00c9VY PROCESSES WITH MARKOV MODULATION"],"prefix":"10.1017","volume":"38","author":[{"given":"Brendan K.","family":"Beare","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Won-Ki","family":"Seo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexis Akira","family":"Toda","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2021,7,13]]},"reference":[{"key":"S0266466621000268_r17","unstructured":"Gouin-Bonenfant, \u00c9. & Toda, A.A. (2020) Pareto extrapolation: An analytical framework for studying tail inequality. Preprint. https:\/\/ssrn.com\/abstract=3260899."},{"key":"S0266466621000268_r19","volume-title":"Matrix Analysis","author":"Horn","year":"2013"},{"key":"S0266466621000268_r44","doi-asserted-by":"publisher","DOI":"10.2307\/2296058"},{"key":"S0266466621000268_r8","unstructured":"Beare, B.K. & Toda, A.A. (2021) Determination of Pareto exponents in economic models driven by Markov multiplicative processes. Preprint. https:\/\/arxiv.org\/abs\/1712.01431."},{"key":"S0266466621000268_r29","doi-asserted-by":"publisher","DOI":"10.2307\/1905384"},{"key":"S0266466621000268_r37","doi-asserted-by":"publisher","DOI":"10.1007\/BF00251419"},{"key":"S0266466621000268_r40","doi-asserted-by":"publisher","DOI":"10.1086\/682729"},{"key":"S0266466621000268_r9","doi-asserted-by":"publisher","DOI":"10.1017\/S1365100514000066"},{"key":"S0266466621000268_r16","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA13569"},{"key":"S0266466621000268_r42","volume-title":"The Laplace Transform","author":"Widder","year":"1941"},{"key":"S0266466621000268_r34","first-page":"607","article-title":"The size distribution of business firms","volume":"48","author":"Simon","year":"1958","journal-title":"American Economic Review"},{"key":"S0266466621000268_r3","first-page":"36","article-title":"Zipf\u2019s law, Pareto\u2019s law, and the evolution of top incomes in the United States","volume":"9","author":"Aoki","year":"2017","journal-title":"American Economic Journal: Macroeconomics"},{"key":"S0266466621000268_r41","doi-asserted-by":"publisher","DOI":"10.1257\/000282803322157179"},{"key":"S0266466621000268_r32","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-08546-2_32"},{"key":"S0266466621000268_r26","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(86)90233-8"},{"key":"S0266466621000268_r30","volume-title":"L\u00e9vy Processes and Infinitely Divisible Distributions","author":"Sato","year":"1999"},{"key":"S0266466621000268_r11","doi-asserted-by":"publisher","DOI":"10.2307\/2227127"},{"key":"S0266466621000268_r35","volume-title":"Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems","author":"Smith","year":"1995"},{"key":"S0266466621000268_r45","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-30709-6"},{"key":"S0266466621000268_r2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jinteco.2016.05.003"},{"key":"S0266466621000268_r7","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2020.132649"},{"key":"S0266466621000268_r23","volume-title":"Characteristic Functions","author":"Lukacs","year":"1970"},{"key":"S0266466621000268_r6","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466619000276"},{"key":"S0266466621000268_r5","volume-title":"Applied Probability and Queues","author":"Asmussen","year":"2003"},{"key":"S0266466621000268_r14","volume-title":"Controlled Markov Processes and Viscosity Solutions","author":"Fleming","year":"2006"},{"key":"S0266466621000268_r15","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466619000306"},{"key":"S0266466621000268_r10","doi-asserted-by":"publisher","DOI":"10.1016\/j.red.2017.10.001"},{"key":"S0266466621000268_r18","volume-title":"Ordinary Differential Equations","author":"Hartman","year":"1982"},{"key":"S0266466621000268_r21","doi-asserted-by":"publisher","DOI":"10.1086\/699190"},{"key":"S0266466621000268_r13","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(75)90038-4"},{"key":"S0266466621000268_r12","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-3037-6"},{"key":"S0266466621000268_r25","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810633"},{"key":"S0266466621000268_r27","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-1765(01)00524-9"},{"key":"S0266466621000268_r28","doi-asserted-by":"publisher","DOI":"10.2307\/1910384"},{"key":"S0266466621000268_r1","doi-asserted-by":"publisher","DOI":"10.1093\/restud\/rdab002"},{"key":"S0266466621000268_r31","first-page":"97","volume-title":"Computational and Combinatorial Methods in Systems Theory","author":"Schumacher","year":"1986"},{"key":"S0266466621000268_r4","doi-asserted-by":"publisher","DOI":"10.1093\/qje\/qjv039"},{"key":"S0266466621000268_r36","doi-asserted-by":"publisher","DOI":"10.1016\/j.jet.2019.04.001"},{"key":"S0266466621000268_r38","doi-asserted-by":"publisher","DOI":"10.1016\/j.jet.2014.09.015"},{"key":"S0266466621000268_r33","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/42.3-4.425"},{"key":"S0266466621000268_r24","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2007.903114"},{"key":"S0266466621000268_r39","doi-asserted-by":"publisher","DOI":"10.1016\/j.jedc.2017.09.002"},{"key":"S0266466621000268_r43","doi-asserted-by":"publisher","DOI":"10.2307\/1905385"},{"key":"S0266466621000268_r20","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(71)90015-1"},{"key":"S0266466621000268_r22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmoneco.2017.11.008"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466621000268","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,22]],"date-time":"2022-11-22T12:31:06Z","timestamp":1669120266000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466621000268\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,13]]},"references-count":45,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["S0266466621000268"],"URL":"https:\/\/doi.org\/10.1017\/s0266466621000268","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,13]]}}}