Stochastic Modelling of Big Data in Finance
portes grátis
Stochastic Modelling of Big Data in Finance
Swishchuk, Anatoliy
Taylor & Francis Ltd
11/2022
280
Dura
Inglês
9781032209265
15 a 20 dias
721
Descrição não disponível.
1. A Brief Introduction: Stochastic Modelling of Big Data in Finance. 1.1. Introduction. 1.2. Big Data in Finance: Limit Order Books. 1.3. Stochastic Modelling of Big Data in Finance: Limit Order Books (LOB). 1.4 Illustration and Justification of Our Method to Study Big Data in Finance. 1.5. Methodological Aspects of Using the Models. 1.6. Conclusion. I. Semi-Markovian Modelling of Big Data in Finance. 2. A Semi-Markovian Modelling of Big Data in Finance. 2.1. Introduction. 2.2. A Semi-Markovian Modeling of Limit Order Markets. 2.3. Main Probabilistic Results. 2.4. Diffusion Limit of the Price Process. 2.5. Numerical Results. 2.6. More Big Data. 2.7. Conclusion. 3. General Semi-Markovian Modelling of Big Data in Finance. 3.1. Introduction. 3.2. Reviewing the Assumptions with Our New Data Sets. 3.3. General Semi-Markov Model for the Limit Order Book with Two States. 3.4. General Semi-Markov Model for the Limit Order Book with arbitrary number of states. 3.5. Discussion on Price Spreads. 3.6. Conclusion. II. Modelling of Big Data in Finance with Hawkes Processes. 4. A Brief Introduction to Hawkes Processes. 4.1. Introduction. 4.2. Definition of Hawkes Processes (HPs). 4.3. Compound Hawkes Processes. 4.4. Limit Theorems for Hawkes Processes: LLN and FCLT. 4.5. Limit Theorems for Poisson Processes: LLN and FCLT. 4.6. Stylized Properties of Hawkes Process. 4.7. Conclusion. 5. Stochastic Modelling of Big Data in Finance with CHP. 5.1. Introduction. 5.2. Definitions of HP, CHP and RSCHP. 5.3. Diffusion Limits and LLNs for CHP and RSCHP in Limit Order Books. 5.4. Numerical Examples and Parameters Estimations. 5.5. Conclusion. 6. Stochastic Modelling of Big Data in Finance with GCHP. 6.1. A Brief Introduction and Literature Review. 6.2. Diffusion Limits and LLNs. 6.3. Empirical Results. 6.4. Conclusion. 7. Quantitative and Comparative Analyses of Big Data with GCHP. 7.1. Introduction. 7.2. Theoretical Analysis. 7.3. Application. 7.4. Hawkes Process and Models Calibrations. 7.5. Error Measurement. 7.6. Conclusion. III. Multivariate Modelling of Big Data in Finance. 8. Multivariate General Compound Hawkes Processes in BDF. 8.1. Introduction. 8.2. Hawkes Processes and Limit Theorems. 8.3. Multivariate General Compound Hawkes Processes (MGCHP) and Limit Theorems. 8.4. FCLT II for MGCHP: Deterministic Centralization. 8.5. Numerical Example. 8.6. Conclusion. 9. Multivariate General Compound Point Processes in BDF. 9.1. Introduction. 9.2. Definition of Multivariate General Compound Point Process (MGCPP). 9.3. LLNs and Diffusion Limits for MGCPP. 9.4. Diffusion Limit for the MGCPP: Deterministic Centralization. 9.5. Conclusion. IV. Appendix: Basics in Stochastic Processes
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Stochastic Modelling;big data in finance;multivariate models;high-frequency and algorithmic trading;limit order books;Mathematical finance;Lob;Hp;FCLT;Skorokhod Topology;Ergodic Probabilities;Inter-arrival Time;Markov Chain;Lob Data;MHP;Excitation Function;Modelling Limit Order Books;Conditional Intensity Function;PSO;Markov Renewal Processes;Tick Size;Ergodic Markov Chain;ACD;Point Process;Empirical CDF;Real Standard Deviation;Standard Deviation Comparisons;Limit Order Market;Multivariate Point Process;Mid Price;Lead Lag Effect
1. A Brief Introduction: Stochastic Modelling of Big Data in Finance. 1.1. Introduction. 1.2. Big Data in Finance: Limit Order Books. 1.3. Stochastic Modelling of Big Data in Finance: Limit Order Books (LOB). 1.4 Illustration and Justification of Our Method to Study Big Data in Finance. 1.5. Methodological Aspects of Using the Models. 1.6. Conclusion. I. Semi-Markovian Modelling of Big Data in Finance. 2. A Semi-Markovian Modelling of Big Data in Finance. 2.1. Introduction. 2.2. A Semi-Markovian Modeling of Limit Order Markets. 2.3. Main Probabilistic Results. 2.4. Diffusion Limit of the Price Process. 2.5. Numerical Results. 2.6. More Big Data. 2.7. Conclusion. 3. General Semi-Markovian Modelling of Big Data in Finance. 3.1. Introduction. 3.2. Reviewing the Assumptions with Our New Data Sets. 3.3. General Semi-Markov Model for the Limit Order Book with Two States. 3.4. General Semi-Markov Model for the Limit Order Book with arbitrary number of states. 3.5. Discussion on Price Spreads. 3.6. Conclusion. II. Modelling of Big Data in Finance with Hawkes Processes. 4. A Brief Introduction to Hawkes Processes. 4.1. Introduction. 4.2. Definition of Hawkes Processes (HPs). 4.3. Compound Hawkes Processes. 4.4. Limit Theorems for Hawkes Processes: LLN and FCLT. 4.5. Limit Theorems for Poisson Processes: LLN and FCLT. 4.6. Stylized Properties of Hawkes Process. 4.7. Conclusion. 5. Stochastic Modelling of Big Data in Finance with CHP. 5.1. Introduction. 5.2. Definitions of HP, CHP and RSCHP. 5.3. Diffusion Limits and LLNs for CHP and RSCHP in Limit Order Books. 5.4. Numerical Examples and Parameters Estimations. 5.5. Conclusion. 6. Stochastic Modelling of Big Data in Finance with GCHP. 6.1. A Brief Introduction and Literature Review. 6.2. Diffusion Limits and LLNs. 6.3. Empirical Results. 6.4. Conclusion. 7. Quantitative and Comparative Analyses of Big Data with GCHP. 7.1. Introduction. 7.2. Theoretical Analysis. 7.3. Application. 7.4. Hawkes Process and Models Calibrations. 7.5. Error Measurement. 7.6. Conclusion. III. Multivariate Modelling of Big Data in Finance. 8. Multivariate General Compound Hawkes Processes in BDF. 8.1. Introduction. 8.2. Hawkes Processes and Limit Theorems. 8.3. Multivariate General Compound Hawkes Processes (MGCHP) and Limit Theorems. 8.4. FCLT II for MGCHP: Deterministic Centralization. 8.5. Numerical Example. 8.6. Conclusion. 9. Multivariate General Compound Point Processes in BDF. 9.1. Introduction. 9.2. Definition of Multivariate General Compound Point Process (MGCPP). 9.3. LLNs and Diffusion Limits for MGCPP. 9.4. Diffusion Limit for the MGCPP: Deterministic Centralization. 9.5. Conclusion. IV. Appendix: Basics in Stochastic Processes
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
Stochastic Modelling;big data in finance;multivariate models;high-frequency and algorithmic trading;limit order books;Mathematical finance;Lob;Hp;FCLT;Skorokhod Topology;Ergodic Probabilities;Inter-arrival Time;Markov Chain;Lob Data;MHP;Excitation Function;Modelling Limit Order Books;Conditional Intensity Function;PSO;Markov Renewal Processes;Tick Size;Ergodic Markov Chain;ACD;Point Process;Empirical CDF;Real Standard Deviation;Standard Deviation Comparisons;Limit Order Market;Multivariate Point Process;Mid Price;Lead Lag Effect
