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Discrete Stochastic Processes : Tools for Machine Learning and Data Science / / by Nicolas Privault
Discrete Stochastic Processes : Tools for Machine Learning and Data Science / / by Nicolas Privault
Autore Privault Nicolas
Edizione [1st ed. 2024.]
Pubbl/distr/stampa Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2024
Descrizione fisica 1 online resource (294 pages)
Disciplina 006.310727
Collana Springer Undergraduate Mathematics Series
Soggetto topico Stochastic processes
Computer science - Mathematics
Stochastic Processes
Mathematical Applications in Computer Science
ISBN 3-031-65820-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto - 1. A Summary of Markov Chains -- 2. Phase-Type Distributions -- 3. Synchronizing Automata -- 4. Random Walks and Recurrence -- 5. Cookie-Excited Random Walks -- 6. Convergence to Equilibrium -- 7. The Ising Model -- 8. Search Engines -- 9. Hidden Markov Model -- 10. Markov Decision Processes.
Record Nr. UNINA-9910896193803321
Privault Nicolas  
Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2024
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
An elementary introduction to stochastic interest rate modeling [[electronic resource] /] / Nicolas Privault
An elementary introduction to stochastic interest rate modeling [[electronic resource] /] / Nicolas Privault
Autore Privault Nicolas
Edizione [2nd ed.]
Pubbl/distr/stampa Hackensack, N.J., : World Scientific, 2012
Descrizione fisica 1 online resource (243 p.)
Disciplina 332.8
332.80151922
Collana Advanced series on statistical science & applied probability
Soggetto topico Interest rate futures - Mathematical models
Stochastic models
Soggetto genere / forma Electronic books.
ISBN 1-281-60363-5
9786613784322
981-4390-86-0
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface; Contents; 1. A Review of Stochastic Calculus; 1.1 Brownian Motion; 1.2 Stochastic Integration; 1.3 Quadratic Variation; 1.4 Ito's Formula; 1.5 Exercises; 2. A Review of Black-Scholes Pricing and Hedging; 2.1 Call and Put Options; 2.2 Market Model and Portfolio; 2.3 PDE Method; 2.4 The Girsanov Theorem; 2.5 Martingale Method; 2.6 Exercises; 3. Short Term Interest Rate Models; 3.1 Mean-Reverting Models; 3.2 Constant Elasticity of Variance (CEV) Models; 3.3 Time-Dependent Models; 3.4 Exercises; 4. Pricing of Zero-Coupon Bonds; 4.1 Definition and Basic Properties
4.2 Absence of Arbitrage and the Markov Property4.3 Absence of Arbitrage and the Martingale Property; 4.4 PDE Solution: Probabilistic Method; 4.5 PDE Solution: Analytical Method; 4.6 Numerical Simulations; 4.7 Exercises; 5. Forward Rate Modeling; 5.1 Forward Contracts; 5.2 Instantaneous Forward Rate; 5.3 Short Rates; 5.4 Parametrization of Forward Rates; Nelson-Siegel parametrization; Svensson parametrization; 5.5 Curve Estimation; 5.6 Exercises; 6. The Heath-Jarrow-Morton (HJM) Model; 6.1 Restatement of Objectives; 6.2 Forward Vasicek Rates; 6.3 Spot Forward Rate Dynamics
6.4 The HJM Condition6.5 Markov Property of Short Rates; 6.6 The Hull-White Model; 6.7 Exercises; 7. The Forward Measure and Derivative Pricing; 7.1 Forward Measure; 7.2 Dynamics under the Forward Measure; 7.3 Derivative Pricing; 7.4 Inverse Change of Measure; 7.5 Exercises; 8. Curve Fitting and a Two-Factor Model; 8.1 Curve Fitting; 8.2 Deterministic Shifts; 8.3 The Correlation Problem; 8.4 Two-Factor Model; 8.5 Exercises; 9. A Credit Default Model; 9.1 Survival Probabilities; 9.2 Stochastic Default; 9.3 Defaultable Bonds; 9.4 Credit Default Swaps; 9.5 Exercises
10. Pricing of Caps and Swaptions on the LIBOR10.1 Pricing of Caplets and Caps; 10.2 Forward Rate Measure and Tenor Structure; 10.3 Swaps and Swaptions; 10.4 The London InterBank Offered Rates (LIBOR) Model; 10.5 Swap Rates on the LIBOR Market; 10.6 Forward Swap Measures; 10.7 Swaption Pricing on the LIBOR Market; 10.8 Exercises; 11. The Brace-Gatarek-Musiela (BGM) Model; 11.1 The BGM Model; 11.2 Cap Pricing; 11.3 Swaption Pricing; 11.4 Calibration of the BGM Model; 11.5 Exercises; 12. Appendix A: Mathematical Tools; Measurability; Covariance and Correlation; Gaussian Random Variables
Conditional ExpectationMartingales in Discrete Time; Martingales in Continuous Time; Markov Processes; 13. Appendix B: Some Recent Developments; Infinite dimensional analysis; Extended interest rate models; Exotic and path-dependent options on interest rates; Sensitivity analysis and the Malliavin calculus; Longevity and mortality risk; 14. Solutions to the Exercises; Bibliography; Index; Author Index
Record Nr. UNINA-9910462558603321
Privault Nicolas  
Hackensack, N.J., : World Scientific, 2012
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
An elementary introduction to stochastic interest rate modeling [[electronic resource] /] / Nicolas Privault
An elementary introduction to stochastic interest rate modeling [[electronic resource] /] / Nicolas Privault
Autore Privault Nicolas
Edizione [2nd ed.]
Pubbl/distr/stampa Hackensack, N.J., : World Scientific, 2012
Descrizione fisica 1 online resource (243 p.)
Disciplina 332.8
332.80151922
Collana Advanced series on statistical science & applied probability
Soggetto topico Interest rate futures - Mathematical models
Stochastic models
ISBN 1-281-60363-5
9786613784322
981-4390-86-0
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface; Contents; 1. A Review of Stochastic Calculus; 1.1 Brownian Motion; 1.2 Stochastic Integration; 1.3 Quadratic Variation; 1.4 Ito's Formula; 1.5 Exercises; 2. A Review of Black-Scholes Pricing and Hedging; 2.1 Call and Put Options; 2.2 Market Model and Portfolio; 2.3 PDE Method; 2.4 The Girsanov Theorem; 2.5 Martingale Method; 2.6 Exercises; 3. Short Term Interest Rate Models; 3.1 Mean-Reverting Models; 3.2 Constant Elasticity of Variance (CEV) Models; 3.3 Time-Dependent Models; 3.4 Exercises; 4. Pricing of Zero-Coupon Bonds; 4.1 Definition and Basic Properties
4.2 Absence of Arbitrage and the Markov Property4.3 Absence of Arbitrage and the Martingale Property; 4.4 PDE Solution: Probabilistic Method; 4.5 PDE Solution: Analytical Method; 4.6 Numerical Simulations; 4.7 Exercises; 5. Forward Rate Modeling; 5.1 Forward Contracts; 5.2 Instantaneous Forward Rate; 5.3 Short Rates; 5.4 Parametrization of Forward Rates; Nelson-Siegel parametrization; Svensson parametrization; 5.5 Curve Estimation; 5.6 Exercises; 6. The Heath-Jarrow-Morton (HJM) Model; 6.1 Restatement of Objectives; 6.2 Forward Vasicek Rates; 6.3 Spot Forward Rate Dynamics
6.4 The HJM Condition6.5 Markov Property of Short Rates; 6.6 The Hull-White Model; 6.7 Exercises; 7. The Forward Measure and Derivative Pricing; 7.1 Forward Measure; 7.2 Dynamics under the Forward Measure; 7.3 Derivative Pricing; 7.4 Inverse Change of Measure; 7.5 Exercises; 8. Curve Fitting and a Two-Factor Model; 8.1 Curve Fitting; 8.2 Deterministic Shifts; 8.3 The Correlation Problem; 8.4 Two-Factor Model; 8.5 Exercises; 9. A Credit Default Model; 9.1 Survival Probabilities; 9.2 Stochastic Default; 9.3 Defaultable Bonds; 9.4 Credit Default Swaps; 9.5 Exercises
10. Pricing of Caps and Swaptions on the LIBOR10.1 Pricing of Caplets and Caps; 10.2 Forward Rate Measure and Tenor Structure; 10.3 Swaps and Swaptions; 10.4 The London InterBank Offered Rates (LIBOR) Model; 10.5 Swap Rates on the LIBOR Market; 10.6 Forward Swap Measures; 10.7 Swaption Pricing on the LIBOR Market; 10.8 Exercises; 11. The Brace-Gatarek-Musiela (BGM) Model; 11.1 The BGM Model; 11.2 Cap Pricing; 11.3 Swaption Pricing; 11.4 Calibration of the BGM Model; 11.5 Exercises; 12. Appendix A: Mathematical Tools; Measurability; Covariance and Correlation; Gaussian Random Variables
Conditional ExpectationMartingales in Discrete Time; Martingales in Continuous Time; Markov Processes; 13. Appendix B: Some Recent Developments; Infinite dimensional analysis; Extended interest rate models; Exotic and path-dependent options on interest rates; Sensitivity analysis and the Malliavin calculus; Longevity and mortality risk; 14. Solutions to the Exercises; Bibliography; Index; Author Index
Record Nr. UNINA-9910790318703321
Privault Nicolas  
Hackensack, N.J., : World Scientific, 2012
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
An elementary introduction to stochastic interest rate modeling / / Nicolas Privault
An elementary introduction to stochastic interest rate modeling / / Nicolas Privault
Autore Privault Nicolas
Edizione [2nd ed.]
Pubbl/distr/stampa Hackensack, N.J., : World Scientific, 2012
Descrizione fisica 1 online resource (243 p.)
Disciplina 332.8
332.80151922
Collana Advanced series on statistical science & applied probability
Soggetto topico Interest rate futures - Mathematical models
Stochastic models
ISBN 1-281-60363-5
9786613784322
981-4390-86-0
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface; Contents; 1. A Review of Stochastic Calculus; 1.1 Brownian Motion; 1.2 Stochastic Integration; 1.3 Quadratic Variation; 1.4 Ito's Formula; 1.5 Exercises; 2. A Review of Black-Scholes Pricing and Hedging; 2.1 Call and Put Options; 2.2 Market Model and Portfolio; 2.3 PDE Method; 2.4 The Girsanov Theorem; 2.5 Martingale Method; 2.6 Exercises; 3. Short Term Interest Rate Models; 3.1 Mean-Reverting Models; 3.2 Constant Elasticity of Variance (CEV) Models; 3.3 Time-Dependent Models; 3.4 Exercises; 4. Pricing of Zero-Coupon Bonds; 4.1 Definition and Basic Properties
4.2 Absence of Arbitrage and the Markov Property4.3 Absence of Arbitrage and the Martingale Property; 4.4 PDE Solution: Probabilistic Method; 4.5 PDE Solution: Analytical Method; 4.6 Numerical Simulations; 4.7 Exercises; 5. Forward Rate Modeling; 5.1 Forward Contracts; 5.2 Instantaneous Forward Rate; 5.3 Short Rates; 5.4 Parametrization of Forward Rates; Nelson-Siegel parametrization; Svensson parametrization; 5.5 Curve Estimation; 5.6 Exercises; 6. The Heath-Jarrow-Morton (HJM) Model; 6.1 Restatement of Objectives; 6.2 Forward Vasicek Rates; 6.3 Spot Forward Rate Dynamics
6.4 The HJM Condition6.5 Markov Property of Short Rates; 6.6 The Hull-White Model; 6.7 Exercises; 7. The Forward Measure and Derivative Pricing; 7.1 Forward Measure; 7.2 Dynamics under the Forward Measure; 7.3 Derivative Pricing; 7.4 Inverse Change of Measure; 7.5 Exercises; 8. Curve Fitting and a Two-Factor Model; 8.1 Curve Fitting; 8.2 Deterministic Shifts; 8.3 The Correlation Problem; 8.4 Two-Factor Model; 8.5 Exercises; 9. A Credit Default Model; 9.1 Survival Probabilities; 9.2 Stochastic Default; 9.3 Defaultable Bonds; 9.4 Credit Default Swaps; 9.5 Exercises
10. Pricing of Caps and Swaptions on the LIBOR10.1 Pricing of Caplets and Caps; 10.2 Forward Rate Measure and Tenor Structure; 10.3 Swaps and Swaptions; 10.4 The London InterBank Offered Rates (LIBOR) Model; 10.5 Swap Rates on the LIBOR Market; 10.6 Forward Swap Measures; 10.7 Swaption Pricing on the LIBOR Market; 10.8 Exercises; 11. The Brace-Gatarek-Musiela (BGM) Model; 11.1 The BGM Model; 11.2 Cap Pricing; 11.3 Swaption Pricing; 11.4 Calibration of the BGM Model; 11.5 Exercises; 12. Appendix A: Mathematical Tools; Measurability; Covariance and Correlation; Gaussian Random Variables
Conditional ExpectationMartingales in Discrete Time; Martingales in Continuous Time; Markov Processes; 13. Appendix B: Some Recent Developments; Infinite dimensional analysis; Extended interest rate models; Exotic and path-dependent options on interest rates; Sensitivity analysis and the Malliavin calculus; Longevity and mortality risk; 14. Solutions to the Exercises; Bibliography; Index; Author Index
Record Nr. UNINA-9910821107503321
Privault Nicolas  
Hackensack, N.J., : World Scientific, 2012
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Stochastic analysis in discrete and continuous settings : with normal martingales / / Nicolas Privault
Stochastic analysis in discrete and continuous settings : with normal martingales / / Nicolas Privault
Autore Privault Nicolas
Edizione [1st ed. 2009.]
Pubbl/distr/stampa Berlin, Germany : , : Springer, , [2009]
Descrizione fisica 1 online resource (321 p.)
Disciplina 519.22
Collana Lecture notes in mathematics
Soggetto topico Stochastic analysis
Space and time
Martingales (Mathematics)
ISBN 1-282-65581-7
9786612655814
3-642-02380-0
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto The Discrete Time Case -- Continuous Time Normal Martingales -- Gradient and Divergence Operators -- Annihilation and Creation Operators -- Analysis on the Wiener Space -- Analysis on the Poisson Space -- Local Gradients on the Poisson Space -- Option Hedging in Continuous Time.
Record Nr. UNINA-9910483837903321
Privault Nicolas  
Berlin, Germany : , : Springer, , [2009]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Stochastic analysis in discrete and continuous settings : with normal martingales / / Nicolas Privault
Stochastic analysis in discrete and continuous settings : with normal martingales / / Nicolas Privault
Autore Privault Nicolas
Edizione [1st ed. 2009.]
Pubbl/distr/stampa Berlin, Germany : , : Springer, , [2009]
Descrizione fisica 1 online resource (321 p.)
Disciplina 519.22
Collana Lecture notes in mathematics
Soggetto topico Stochastic analysis
Space and time
Martingales (Mathematics)
ISBN 1-282-65581-7
9786612655814
3-642-02380-0
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto The Discrete Time Case -- Continuous Time Normal Martingales -- Gradient and Divergence Operators -- Annihilation and Creation Operators -- Analysis on the Wiener Space -- Analysis on the Poisson Space -- Local Gradients on the Poisson Space -- Option Hedging in Continuous Time.
Record Nr. UNISA-996466768903316
Privault Nicolas  
Berlin, Germany : , : Springer, , [2009]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Understanding Markov Chains : Examples and Applications / / by Nicolas Privault
Understanding Markov Chains : Examples and Applications / / by Nicolas Privault
Autore Privault Nicolas
Edizione [2nd ed. 2018.]
Pubbl/distr/stampa Singapore : , : Springer Singapore : , : Imprint : Springer, , 2018
Descrizione fisica 1 online resource (XVII, 372 p. 44 illus.)
Disciplina 519.233
Collana Springer Undergraduate Mathematics Series
Soggetto topico Probabilities
Statistics 
Probability Theory and Stochastic Processes
Statistical Theory and Methods
Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences
ISBN 978-981-13-0659-4
981-13-0659-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Probability Background -- Gambling Problems -- Random Walks -- Discrete-Time Markov Chains -- First Step Analysis -- Classification of States -- Long-Run Behavior of Markov Chains -- Branching Processes -- Continuous-Time Markov Chains -- Discrete-Time Martingales -- Spatial Poisson Processes -- Reliability Theory.
Record Nr. UNINA-9910300101903321
Privault Nicolas  
Singapore : , : Springer Singapore : , : Imprint : Springer, , 2018
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Understanding Markov Chains : Examples and Applications / / by Nicolas Privault
Understanding Markov Chains : Examples and Applications / / by Nicolas Privault
Autore Privault Nicolas
Edizione [1st ed. 2013.]
Pubbl/distr/stampa Singapore : , : Springer Singapore : , : Imprint : Springer, , 2013
Descrizione fisica 1 online resource (357 p.)
Disciplina 519.233
Collana Springer Undergraduate Mathematics Series
Soggetto topico Probabilities
Statistics 
Probability Theory and Stochastic Processes
Statistical Theory and Methods
Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences
ISBN 981-4451-51-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Introduction -- 1) Probability Background -- 2) Gambling Problems -- 3) Random Walks -- 4) Discrete-Time Markov Chains -- 5) First Step Analysis -- 6) Classication of States -- 7) Long-Run Behavior of Markov Chains -- 8) Branching Processes -- 9) Continuous-Time Markov Chains -- 10) Discrete-Time Martingales -- 11) Spatial Poisson Processes -- 12) Reliability Theory -- Some Useful Identities -- Solutions to the Exercises -- References -- Index.
Record Nr. UNINA-9910438037003321
Privault Nicolas  
Singapore : , : Springer Singapore : , : Imprint : Springer, , 2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui