LEADER 04056nam 2200697 450 001 9910788816603321 005 20210422201815.0 010 $a3-11-038990-8 010 $a3-11-032984-0 024 7 $a10.1515/9783110329841 035 $a(CKB)3360000000515049 035 $a(EBL)1663085 035 $a(SSID)ssj0001431854 035 $a(PQKBManifestationID)11791785 035 $a(PQKBTitleCode)TC0001431854 035 $a(PQKBWorkID)11387855 035 $a(PQKB)11645696 035 $a(DE-B1597)211998 035 $a(OCoLC)903573040 035 $a(DE-B1597)9783110329841 035 $a(Au-PeEL)EBL1663085 035 $a(CaPaEBR)ebr11015800 035 $a(CaONFJC)MIL807674 035 $a(CaSebORM)9783110329681 035 $a(MiAaPQ)EBC1663085 035 $a(PPN)187993696 035 $a(EXLCZ)993360000000515049 100 $a20150212h20152015 uy 0 101 0 $aeng 135 $aur|nu---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aAmerican-type options$hVolume 2$iStochastic approximation methods /$fDmitrii S. Silvestrov 210 1$aBerlin, Germany :$cDe Gruyter,$d2015. 210 4$dİ2015 215 $a1 online resource (572 p.) 225 1 $aDe Gruyter Studies in Mathematics,$x0179-0986 ;$vVolume 57 300 $aDescription based upon print version of record. 311 $a3-11-032985-9 311 $a3-11-032968-9 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tPreface --$tContents --$t1 Reward approximations for autoregressive log-price processes (LPP) --$t2 Reward approximations for autoregressive stochastic volatility LPP --$t3 American-type options for continuous time Markov LPP --$t4 Upper bounds for option rewards for Markov LPP --$t5 Time-skeleton reward approximations for Markov LPP --$t6 Time-space-skeleton reward approximations for Markov LPP --$t7 Convergence of option rewards for continuous time Markov LPP --$t8 Convergence of option rewards for diffusion LPP --$t9 European, knockout, reselling and random pay-off options --$t10 Results of experimental studies --$tBibliographical Remarks --$tBibliography --$tIndex --$tDe Gruyter Studies in Mathematics 330 $aThe book gives a systematical presentation of stochastic approximation methods for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The volume presents results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies. 410 0$aDe Gruyter studies in mathematics ;$vVolume 57. 606 $aOptions (Finance)$xMathematical models 606 $aStochastic approximation 606 $aBusiness mathematics 610 $aAmerican option, Optimal stopping, Convergence of rewards, Markov chain, Approximation algorithm. 615 0$aOptions (Finance)$xMathematical models. 615 0$aStochastic approximation. 615 0$aBusiness mathematics. 676 $a332.6453 700 $aSilvestrov$b Dmitrii S.$0740587 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788816603321 996 $aAmerican-type options$91468593 997 $aUNINA