Jiaming Chen, NYU Shanghai<\/p>\n\n\n\n
Title:\u00a0<\/strong>New stochastic Fubini theorem of measure-valued processes\u00a0via stochastic\u00a0integration<\/em><\/p>\n\n\n\n Abstract:<\/strong><\/em><\/p>\n\n\n\n Classical stochastic Fubini theorems start from a fixed semimartingale S, say, and a family of integrands for S which are parametrized by a parameter z, say, from some parameter space Z. There is a (non- random) measure \u03bc, say, on Z, and the stochastic Fubini theorem then says that integration with respect to \u03bc and stochastic integration with respect to S can be interchanged. In other words, we can either 1) first integrate the parametrized integrands with respect to \u03bc and then stochastically integrate the resulting process with respect to S, or we can 2) first stochastically integrate, for each z, the corresponding integrand with respect to S and then integrate the result with respect to \u03bc \u2013 and both double integrals yield the same result. What happens now if we replace the fixed measure \u03bc by a stochastic kernel from the predictable sigma- field to Z? Approach 1) still makes sense, but how about 2)? And can we still get some kind of stochastic Fubini theorem? We show that we can, but we need to define for that a stochastic integral, with respect to S, of suitable measure-valued processes. The origin of this question comes from a (still open) question in mathematical finance. There are also some connections to a class of Volterra-type semimartingales. Based on joint work with Tahir Choulli and Martin Schweizer.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":" Jiaming Chen, NYU Shanghai Title:\u00a0New stochastic Fubini theorem of measure-valued processes\u00a0via stochastic\u00a0integration Abstract: Classical stochastic Fubini theorems start from a fixed semimartingale S, say, and a family of integrands for S which are parametrized by a parameter z, say, from some parameter space Z. There is a (non- random) measure \u03bc, say, on Z, and the […]<\/p>\n","protected":false},"author":16,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-532","post","type-post","status-publish","format-standard","hentry","category-probability_seminar"],"_links":{"self":[{"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/posts\/532","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/users\/16"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/comments?post=532"}],"version-history":[{"count":1,"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/posts\/532\/revisions"}],"predecessor-version":[{"id":533,"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/posts\/532\/revisions\/533"}],"wp:attachment":[{"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/media?parent=532"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/categories?post=532"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pages.charlotte.edu\/probability-seminar\/wp-json\/wp\/v2\/tags?post=532"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}