Pathwise estimation and inference for diffusion market models discusses contemporary techniques for inferring, from options and bond prices, the market participants' aggregate view on important financial parameters such as implied volatility, discount rate, future interest rate, and their uncertainty thereof. The focus is on the pathwise inference methods that are applicable to a sole path of the observed prices and do not require the observation of an ensemble of such paths. This book is pitched at the level of senior undergraduate students undertaking research at honors year, and postgraduate candidates undertaking Master's or PhD degree by research. From a research perspective, this book reaches out to academic researchers from backgrounds as diverse as mathematics and probability, econometrics and statistics, and computational mathematics and optimization whose interest lie in analysis and modelling of financial market data from a multi-disciplinary approach. Additionally, this book is also aimed at financial market practitioners participating in capital market facing businesses who seek to keep abreast with and draw inspiration from novel approaches in market data analysis. The first two chapters of the book contains introductory material on stochastic analysis and the classical diffusion stock market models. The remaining chapters discuss more special stock and bond market models and special methods of pathwise inference for market parameter for different models. The final chapter describes applications of numerical methods of inference of bond market parameters to forecasting of short rate. Nikolai Dokuchaev is an associate professor in Mathematics and Statistics at Curtin University. His research interests include mathematical and statistical finance, stochastic analysis, PDEs, control, and signal processing. Lin Yee Hin is a practitioner in the capital market facing industry. His research interests include econometrics, non-parametric regression, and scientific computing.

This book provides a systematic, self-sufficient and yet short presentation of the mainstream topics on introductory Probability Theory with some selected topics from Mathematical Statistics. It is suitable for a 10- to 14-week course for second- or third-year undergraduate students in Science, Mathematics, Statistics, Finance, or Economics, who have completed some introductory course in Calculus. There is a sufficient number of problems and solutions to cover weekly tutorials.

Dynamic Portfolio Strategies: Quantitative Methods and Empirical Rules for Incomplete Information investigates optimal investment problems for stochastic financial market models. It is addressed to academics and students who are interested in the mathematics of finance, stochastic processes, and optimal control, and also to practitioners in risk management and quantitative analysis who are interested in new strategies and methods of stochastic analysis.

While there are many works devoted to the solution of optimal investment problems for various models, the focus of this book is on analytical strategies based on "technical analysis" which are model-free. The technical analysis of these strategies has a number of characteristics. Two of the more important characteristics are: (1) they require only historical data, and (2) typically they are more widely used by traders than analysis based on stochastic models. Hence it is the objective of this book to reduce the gap between model-free strategies and strategies that are "optimal" for stochastic models. We hope that researchers, students and practitioners will be interested in some of the new empirically based methods of "technical analysis" strategies suggested in this book and evaluated via stochastic market models.

Pathwise estimation and inference for diffusion market models discusses contemporary techniques for inferring, from options and bond prices, the market participants' aggregate view on important financial parameters such as implied volatility, discount rate, future interest rate, and their uncertainty thereof. The focus is on the pathwise inference methods that are applicable to a sole path of the observed prices and do not require the observation of an ensemble of such paths. This book is pitched at the level of senior undergraduate students undertaking research at honors year, and postgraduate candidates undertaking Master's or PhD degree by research. From a research perspective, this book reaches out to academic researchers from backgrounds as diverse as mathematics and probability, econometrics and statistics, and computational mathematics and optimization whose interest lie in analysis and modelling of financial market data from a multi-disciplinary approach. Additionally, this book is also aimed at financial market practitioners participating in capital market facing businesses who seek to keep abreast with and draw inspiration from novel approaches in market data analysis. The first two chapters of the book contains introductory material on stochastic analysis and the classical diffusion stock market models. The remaining chapters discuss more special stock and bond market models and special methods of pathwise inference for market parameter for different models. The final chapter describes applications of numerical methods of inference of bond market parameters to forecasting of short rate. Nikolai Dokuchaev is an associate professor in Mathematics and Statistics at Curtin University. His research interests include mathematical and statistical finance, stochastic analysis, PDEs, control, and signal processing. Lin Yee Hin is a practitioner in the capital market facing industry. His research interests include econometrics, non-parametric regression, and scientific computing.

Written in a rigorous yet logical and easy to use style, spanning a range of disciplines, including business, mathematics, finance and economics, this comprehensive textbook offers a systematic, self-sufficient yet concise presentation of the main topics and related parts of Stochastic Analysis and statistical finance that are covered in the majority of university programmes.

Providing all explanations of basic concepts and results with proofs and numerous examples and problems, it includes:

• an introduction to probability theory
• a detailed study of discrete and continuous time market models
• a comprehensive review of Ito calculus and statistical methods as a basis for statistical estimation of models for pricing
• a detailed discussion of options and their pricing, including American options in continuous time setting.

An excellent introduction to the topic, this textbook is an essential resource for all students on undergraduate and postgraduate courses and advanced degree programs in econometrics, finance, applied mathematics and mathematical modelling as well as academics and practitioners.

Written in a rigorous yet logical and easy to use style, spanning a range of disciplines, including business, mathematics, finance and economics, this comprehensive textbook offers a systematic, self-sufficient yet concise presentation of the main topics and related parts of Stochastic Analysis and statistical finance that are covered in the majority of university programmes.

Providing all explanations of basic concepts and results with proofs and numerous examples and problems, it includes:

• an introduction to probability theory
• a detailed study of discrete and continuous time market models
• a comprehensive review of Ito calculus and statistical methods as a basis for statistical estimation of models for pricing
• a detailed discussion of options and their pricing, including American options in continuous time setting.

An excellent introduction to the topic, this textbook is an essential resource for all students on undergraduate and postgraduate courses and advanced degree programs in econometrics, finance, applied mathematics and mathematical modelling as well as academics and practitioners.

Dynamic Portfolio Strategies: Quantitative Methods and Empirical Rules for Incomplete Information investigates optimal investment problems for stochastic financial market models. It is addressed to academics and students who are interested in the mathematics of finance, stochastic processes, and optimal control, and also to practitioners in risk management and quantitative analysis who are interested in new strategies and methods of stochastic analysis. While there are many works devoted to the solution of optimal investment problems for various models, the focus of this book is on analytical strategies based on "technical analysis" which are model-free. The technical analysis of these strategies has a number of characteristics. Two of the more important characteristics are: (1) they require only historical data, and (2) typically they are more widely used by traders than analysis based on stochastic models. Hence it is the objective of this book to reduce the gap between model-free strategies and strategies that are "optimal" for stochastic models. We hope that researchers, students and practitioners will be interested in some of the new empirically based methods of "technical analysis" strategies suggested in this book and evaluated via stochastic market models.