{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:32:31Z","timestamp":1787322751656,"version":"build-2736575974"},"reference-count":40,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>A firm issues a convertible bond. At each subsequent time, the bondholder must decide whether to continue to hold the bond, thereby collecting coupons, or to convert it to stock. The bondholder wishes to choose a conversion strategy to maximize the bond value. Subject to some restrictions, the bond can be called by the issuing firm, which presumably acts to maximize the equity value of the firm by minimizing the bond value. This creates a two\u2010person game. We show that if the coupon rate is below the interest rate times the call price, then conversion should precede call. On the other hand, if the dividend rate times the call price is below the coupon rate, call should precede conversion. In either case, the game reduces to a problem of optimal stopping.<\/jats:p>","DOI":"10.1137\/050630222","type":"journal-article","created":{"date-parts":[[2006,10,23]],"date-time":"2006-10-23T11:30:50Z","timestamp":1161603050000},"page":"1508-1539","source":"Crossref","is-referenced-by-count":51,"title":["A Two\u2010Person Game for Pricing Convertible Bonds"],"prefix":"10.1137","volume":"45","author":[{"given":"Mihai","family":"S\u00eerbu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Steven E.","family":"Shreve","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,10,20]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.21314\/JCF.2003.124"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1995.tb04058.x"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1991.tb04618.x"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.3905\/jod.2003.319208"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1080\/10451120290008557"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"P. 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Zhang, eds., AMS\/IP Stud. Adv. Math. 26, Amer. Math. Soc., Providence, RI, 2002, pp. 45\u201358.","DOI":"10.1090\/amsip\/026\/05"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1007\/BF01450498"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/0304-405X(89)90059-7"},{"key":"R17","unstructured":"W. Fleming and H. M. Soner,\n                      Controlled Markov Processes and Viscosity Solutions\n                      , Springer, New York, 1993."},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4149(81)90026-0"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1985.tb02382.x"},{"key":"R20","doi-asserted-by":"crossref","unstructured":"C. Hennessy and Y. Tserlukevich,\n                      Analyzing Callable and Convertible Bonds when the Modigliani\u2010Miller Assumptions are Violated\n                      , EFA Moscow Meetings Paper, Haas School, University California at Berkeley, Berkeley, CA, 2005.","DOI":"10.2139\/ssrn.676161"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.2469\/faj.v52.n5.2022"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1016\/0304-405X(77)90004-6"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-6261.1977.tb03285.x"},{"key":"R24","unstructured":"J. Kallsen and C. K\u00fchn,\n                      Convertible bonds: Financial derivatives of game type\n                      , in Exotic Option Pricing and Advanced L\u00e9vy Models, A. Kyprianov, W. Schoutems, and P. Willmott, eds., Wiley, New York, 2005, pp. 277\u2013292."},{"key":"R25","doi-asserted-by":"crossref","unstructured":"I. Karatzas and S. 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Yigitbasioglu,\n                      Pricing Convertible Bonds with Interest Rate, Equity, Credit and FX Risk\n                      , EFMA London Meeting Paper, ISMA Center, University of Reading, Reading, UK, 2002.","DOI":"10.2139\/ssrn.294464"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/050630222","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:25:11Z","timestamp":1787318711000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/050630222"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":40,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/050630222"],"URL":"https:\/\/doi.org\/10.1137\/050630222","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}