{"id":301,"date":"2018-11-28T15:54:12","date_gmt":"2018-11-28T15:54:12","guid":{"rendered":"http:\/\/blogs.kent.ac.uk\/pgrseminars\/?p=301"},"modified":"2018-11-28T15:54:12","modified_gmt":"2018-11-28T15:54:12","slug":"23-november-jorge-gonzalez","status":"publish","type":"post","link":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/2018\/11\/28\/23-november-jorge-gonzalez\/","title":{"rendered":"23 November ~ Jorge Gonzalez"},"content":{"rendered":"<p><strong>Title:\u00a0<\/strong>Geometrically convergent simulation of the extrema of L\u00e9vy processes<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Abstract:\u00a0<\/strong>We develop a novel Monte Carlo algorithm for the simulation from the joint law of the position, the running supremum and the time of the supremum of a general L\u00e9vy process at an arbitrary finite time. We prove that the bias decays geometrically, in contrast to the power law for the random walk approximation (RWA). We identify the law of the error and, inspired by the recent work of Ivanovs (Zooming in on a Le\u0301vy process at its supremum, Ann. Appl. Probab. 28 (2018)) on RWA, characterise its asymptotic behaviour. We prove that the multilevel Monte Carlo (MLMC) estimator has optimal computational complexity (i.e. of order 1\/\u03b5^2 if the L2-norm of the error is at most \u03b5) for locally Lipschitz and barrier-type functionals of the triplet. If the increments of the L\u00e9vy process cannot be sampled directly, we combine our algorithm with the Asmussen-Rosi\u0144ski approximation by choosing the rate of decay of the cutoff level for small jumps so that the corresponding MC and MLMC estimators have minimal computational complexity.\u00a0<strong>arXiv:1810.11039<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Title:\u00a0Geometrically convergent simulation of the extrema of L\u00e9vy processes &nbsp; Abstract:\u00a0We develop a novel Monte Carlo algorithm for the simulation from the joint law of &hellip; <a href=\"https:\/\/blogs.kent.ac.uk\/pgrseminars\/2018\/11\/28\/23-november-jorge-gonzalez\/\">Read&nbsp;more<\/a><\/p>\n","protected":false},"author":57430,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[170526],"tags":[],"_links":{"self":[{"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/posts\/301"}],"collection":[{"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/users\/57430"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/comments?post=301"}],"version-history":[{"count":1,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/posts\/301\/revisions"}],"predecessor-version":[{"id":302,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/posts\/301\/revisions\/302"}],"wp:attachment":[{"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/media?parent=301"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/categories?post=301"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/pgrseminars\/wp-json\/wp\/v2\/tags?post=301"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}