{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,9]],"date-time":"2024-07-09T09:13:37Z","timestamp":1720516417077},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. Game Theory Rev."],"published-print":{"date-parts":[[2004,3]]},"abstract":"<jats:p> Viability theory can be applied for determining viable capture basin for control problem in presence of uncertainty. We first recall the concepts of viability theory which allow to develop numerical methods for computing viable capture basin for control problems and guaranteed control problems. Recent developments of option pricing in the framework of dynamical games with constraints lead to the formulation of guaranteed valuation in terms of guaranteed viable-capture basin of a dynamical game. As an application we show how the viability\/capturability algorithm evaluates and manages portfolios. Regarding viability\/capturability issues, stochastic control is a particular use of tychastic control. We replace the standard translation of uncertainty by stochastic control problem by tychastic ones and the concept of stochastic viability by the one of guaranteed viability kernel. Considering the Cox\u2013Rubinstein model, we extend algorithms for hedging portfolios in the presence of transaction costs and dividends using recent developments on hybrid calculus. <\/jats:p>","DOI":"10.1142\/s0219198904000101","type":"journal-article","created":{"date-parts":[[2004,5,3]],"date-time":"2004-05-03T05:19:26Z","timestamp":1083561566000},"page":"109-136","source":"Crossref","is-referenced-by-count":13,"title":["VIABLE CAPTURE BASIN FOR STUDYING DIFFERENTIAL AND HYBRID GAMES: APPLICATION TO FINANCE"],"prefix":"10.1142","volume":"06","author":[{"given":"PATRICK","family":"SAINT-PIERRE","sequence":"first","affiliation":[{"name":"Centre de Recherche Viabilit\u00e9, Jeux, Contr\u00f4le Universit\u00e9, Paris-Dauphine, F-75016 Paris, France"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"Viability Theory","author":"Aubin J.-P.","year":"1991"},{"key":"rf2","author":"Aubin J.-P.","journal-title":"SIAM J. Control"},{"key":"rf3","series-title":"Lecture Notes","volume-title":"Impulse differential inclusions and hybrid systems: a viability approach","author":"Aubin J.-P.","year":"1999"},{"key":"rf5","volume-title":"Optimal Control et Partial Differential Equations","author":"Bernhard P.","year":"2000"},{"key":"rf6","volume-title":"A Robust Control Approach to Option Pricing","author":"Bernhard P.","year":"2000"},{"key":"rf7","series-title":"Annals of Dynamic Games","volume-title":"Robust control approach to option pricing, including co\u00fbt de transaction","author":"Bernhard P.","year":"2002"},{"key":"rf8","first-page":"1543","volume":"321","author":"Cardaliaguet P.","journal-title":"Comptes-Rendus de l'Acad\u00e9mie des Sciences"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1592-9_4"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012998349327"},{"key":"rf11","author":"Frankowska H.","journal-title":"SIAM J. on Control and Optimization"},{"key":"rf13","volume-title":"Valuation et gestion dynamiques de portefeuilles","author":"Pujal D.","year":"2000"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01204182"}],"container-title":["International Game Theory Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219198904000101","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T09:23:04Z","timestamp":1565169784000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219198904000101"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,3]]},"references-count":12,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2004,3]]}},"alternative-id":["10.1142\/S0219198904000101"],"URL":"https:\/\/doi.org\/10.1142\/s0219198904000101","relation":{},"ISSN":["0219-1989","1793-6675"],"issn-type":[{"value":"0219-1989","type":"print"},{"value":"1793-6675","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,3]]}}}