American-type options. Vol. 1, Stochastic approximation methods /

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This 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. It is the first volume of the comprehensive two volumes monograph.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Silʹvestrov, D. S. (Dmitriĭ Sergeevich)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin ; Boston : De Gruyter, ©2014.
Colección:De Gruyter studies in mathematics ; 56.
Temas:
Options (Finance) > Mathematical models.
Stochastic approximation.
Markov processes.
Markov Chains
Options (Finances) > Modèles mathématiques.
Approximation stochastique.
Processus de Markov.
Markov processes
Options (Finance) > Mathematical models
Stochastic approximation
American Option.
Approximation Algorithm.
Convergence of Rewards.
Markov Chain.
Optimal Stopping.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Preface; 1 Multivariate modulated Markov log-price processes (LPP); 1.1 Markov LPP; 1.2 LPP represented by random walks; 1.3 Autoregressive LPP; 1.4 Autoregressive stochastic volatility LPP; 2 American-type options; 2.1 American-type options; 2.2 Pay-off functions; 2.3 Reward and log-reward functions; 2.4 Optimal stopping times; 2.5 American-type knockout options; 3 Backward recurrence reward algorithms; 3.1 Binomial tree reward algorithms; 3.2 Trinomial tree reward algorithms; 3.3 Random walk reward algorithms; 3.4 Markov chain reward algorithms; 4 Upper bounds for option rewards.
  • 4.1 Markov LPP with bounded characteristics4.2 LPP represented by random walks; 4.3 Markov LPP with unbounded characteristics; 4.4 Univariate Markov Gaussian LPP; 4.5 Multivariate modulated Markov Gaussian LPP; 5 Convergence of option rewards
  • I; 5.1 Asymptotically uniform upper bounds for rewards
  • I; 5.2 Modulated Markov LPP with bounded characteristics; 5.3 LPP represented by modulated random walks; 6 Convergence of option rewards
  • II; 6.1 Asymptotically uniform upper bounds for rewards
  • II; 6.2 Univariate modulated LPP with unbounded characteristics.
  • 6.3 Asymptotically uniform upper bounds for rewards
  • III6.4 Multivariate modulated LPP with unbounded characteristics; 6.5 Conditions of convergence for Markov price processes; 7 Space-skeleton reward approximations; 7.1 Atomic approximation models; 7.2 Univariate Markov LPP with bounded characteristics; 7.3 MultivariateMarkov LPP with bounded characteristics; 7.4 LPP represented by multivariate modulated random walks; 7.5 MultivariateMarkov LPP with unbounded characteristics; 8 Convergence of rewards for Markov Gaussian LPP; 8.1 Univariate Markov Gaussian LPP.
  • 8.2 Multivariate modulated Markov Gaussian LPP8.3 Markov Gaussian LPP with estimated characteristics; 8.4 Skeleton reward approximations for Markov Gaussian LPP; 8.5 LPP represented by Gaussian random walks; 9 Tree-type approximations for Markov Gaussian LPP; 9.1 Univariate binomial tree approximations; 9.2 Multivariate binomial tree approximations; 9.3 Multivariate trinomial tree approximations; 9.4 Inhomogeneous in space binomial approximations; 9.5 Inhomogeneous in time and space trinomial approximations; 10 Convergence of tree-type reward approximations.
  • 10.1 Univariate binomial tree approximation models10.2 Multivariate homogeneous in space tree models; 10.3 Univariate inhomogeneous in space tree models; 10.4 Multivariate inhomogeneous in space tree models; Bibliographical Remarks; Bibliography; Index.

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