LEADER 04243nam 2200769 450 001 9910814311003321 005 20211208221709.0 010 $a3-11-032982-4 024 7 $a10.1515/9783110329827 035 $a(CKB)2670000000495628 035 $a(EBL)1575440 035 $a(OCoLC)865333012 035 $a(SSID)ssj0001060564 035 $a(PQKBManifestationID)11550861 035 $a(PQKBTitleCode)TC0001060564 035 $a(PQKBWorkID)11088108 035 $a(PQKB)10519507 035 $a(MiAaPQ)EBC1575440 035 $a(DE-B1597)211996 035 $a(OCoLC)1013955008 035 $a(OCoLC)979690012 035 $a(DE-B1597)9783110329827 035 $a(Au-PeEL)EBL1575440 035 $a(CaPaEBR)ebr10820058 035 $a(CaONFJC)MIL804615 035 $a(OCoLC)913854944 035 $a(PPN)182942368 035 $a(EXLCZ)992670000000495628 100 $a20140107h20142014 uy| 0 101 0 $aeng 135 $aurnn#---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aAmerican-type options $estochastic approximation methods. Volume 1 /$fDmitrii S. Silvestrov 210 1$aBerlin :$cDe Gruyter,$d[2014] 210 4$dİ2014 215 $a1 online resource (520 p.) 225 1 $aDe Gruyter studies in mathematics,$x0179-0986 ;$vvolume 56 300 $aDescription based upon print version of record. 311 0 $a3-11-032967-0 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tPreface --$tContents --$t1. Multivariate modulated Markov log-price processes (LPP) --$t2. American-type options --$t3. Backward recurrence reward algorithms --$t4. Upper bounds for option rewards --$t5. Convergence of option rewards - I --$t6. Convergence of option rewards - II --$t7. Space-skeleton reward approximations --$t8. Convergence of rewards for Markov Gaussian LPP --$t9. Tree-type approximations for Markov Gaussian LPP --$t10. Convergence of tree-type reward approximations --$tBibliographical Remarks --$tBibliography --$tIndex --$tBack matter 330 $aThe book gives a systematical presentation of stochastic approximation methods for models of American-type options with general pay-off functions for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The book also contains an extended bibliography of works in the area. This book is the first volume of the comprehensive two volumes monograph. The second volume will present results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies. 410 0$aDe Gruyter studies in mathematics ;$v56. 606 $aOptions (Finance)$xMathematical models 606 $aStochastic approximation 606 $aMarkov processes 606 $aBusiness mathematics 610 $aAmerican Option. 610 $aApproximation Algorithm. 610 $aConvergence of Rewards. 610 $aMarkov Chain. 610 $aOptimal Stopping. 615 0$aOptions (Finance)$xMathematical models. 615 0$aStochastic approximation. 615 0$aMarkov processes. 615 0$aBusiness mathematics. 676 $a332.6/01/5195 700 $aSilvestrov$b Dmitrii S$0740587 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910814311003321 996 $aAmerican-type options$91468593 997 $aUNINA