GUOJUN GAN, PHD, ASA, is Director of Quantitative Modeling and Model Efficiency at Manulife Financial, Canada. His research interests include empirical corporate finance, actuarial science, risk management, data mining, and big data analysis.CHAOQUN MA, PHD, is Professor and Dean of the School of Business Administration at Hunan University, China. The recipient of First Prize in Outstanding Achievements in Teaching in 2009, Dr. Ma’s research interests include financial engineering, risk management, and data mining.HONG XIE, PHD, is Adjunct Professor in the Department of Mathematics and Statistics at York University as well as Vice President of Models and Analytics at Manulife Financial, Canada. Dr. Xie is on the Board of Directors for the Canadian-Chinese Finance Association, and his research interests include financial engineering, mathematical finance, and partial differential equations.

• Preface xviiFinancial Glossary xxiiPart I Measure Theory1 Sets and Sequences 32 Measures 153 Extension of Measures 294 Lebesgue-Stieltjes Measures 375 Measurable Functions 476 Lebesgue Integration 577 The Radon-Nikodym Theorem 778 LP Spaces 859 Convergence 9710 Product Measures 113Part II Probability Theory11 Events and Random Variables 12712 Independence 14113 Expectation 16114 Conditional Expectation 17315 Inequalities 18916 Law of Large Numbers 19917 Characteristic Functions 21718 Discrete Distributions 22719 Continuous Distributions 23920 Central Limit Theorems 257Part III Stochastic Processes21 Stochastic Processes 27122 Martingales 29123 Stopping Times 30124 Martingale Inequalities 32125 Martingale Convergence Theorems 33326 Random Walks 34327 Poisson Processes 35728 Brownian Motion 37329 Markov Processes 38930 Lévy Processes 401Part IV Stochastic Calculus31 The Wiener Integral 42132 The Itô Integral 43133 Extension of the Itô Integral 45334 Martingale Stochastic Integrals 46335 The Itô Formula 47736 Martingale Representation Theorem 49537 Change of Measure 50338 Stochastic Differential Equations 51539 Diffusion 53140 The Feynman-Kac Formula 547Part V Stochastic Financial Models41 Discrete-Time Models 56142 Black-Scholes Option Pricing Models 57943 Path-Dependent Options 59344 American Options 60945 Short Rate Models 62946 Instantaneous Forward Rate Models 64747 LIBOR Market Models 667References 687List of Symbols 703Subject Index 707

GUOJUN GAN, PHD, ASA, is Director of Quantitative Modeling and Model Efficiency at Manulife Financial, Canada. His research interests include empirical corporate finance, actuarial science, risk management, data mining, and big data analysis.CHAOQUN MA, PHD, is Professor and Dean of the School of Business Administration at Hunan University, China. The recipient of First Prize in Outstanding Achievements in Teaching in 2009, Dr. Ma’s research interests include financial engineering, risk management, and data mining.HONG XIE, PHD, is Adjunct Professor in the Department of Mathematics and Statistics at York University as well as Vice President of Models and Analytics at Manulife Financial, Canada. Dr. Xie is on the Board of Directors for the Canadian-Chinese Finance Association, and his research interests include financial engineering, mathematical finance, and partial differential equations.

• Preface xviiFinancial Glossary xxiiPart I Measure Theory1 Sets and Sequences 32 Measures 153 Extension of Measures 294 Lebesgue-Stieltjes Measures 375 Measurable Functions 476 Lebesgue Integration 577 The Radon-Nikodym Theorem 778 LP Spaces 859 Convergence 9710 Product Measures 113Part II Probability Theory11 Events and Random Variables 12712 Independence 14113 Expectation 16114 Conditional Expectation 17315 Inequalities 18916 Law of Large Numbers 19917 Characteristic Functions 21718 Discrete Distributions 22719 Continuous Distributions 23920 Central Limit Theorems 257Part III Stochastic Processes21 Stochastic Processes 27122 Martingales 29123 Stopping Times 30124 Martingale Inequalities 32125 Martingale Convergence Theorems 33326 Random Walks 34327 Poisson Processes 35728 Brownian Motion 37329 Markov Processes 38930 Lévy Processes 401Part IV Stochastic Calculus31 The Wiener Integral 42132 The Itô Integral 43133 Extension of the Itô Integral 45334 Martingale Stochastic Integrals 46335 The Itô Formula 47736 Martingale Representation Theorem 49537 Change of Measure 50338 Stochastic Differential Equations 51539 Diffusion 53140 The Feynman-Kac Formula 547Part V Stochastic Financial Models41 Discrete-Time Models 56142 Black-Scholes Option Pricing Models 57943 Path-Dependent Options 59344 American Options 60945 Short Rate Models 62946 Instantaneous Forward Rate Models 64747 LIBOR Market Models 667References 687List of Symbols 703Subject Index 707

GUOJUN GAN, PHD, ASA, is Director of Quantitative Modeling and Model Efficiency at Manulife Financial, Canada. His research interests include empirical corporate finance, actuarial science, risk management, data mining, and big data analysis.CHAOQUN MA, PHD, is Professor and Dean of the School of Business Administration at Hunan University, China. The recipient of First Prize in Outstanding Achievements in Teaching in 2009, Dr. Ma’s research interests include financial engineering, risk management, and data mining.HONG XIE, PHD, is Adjunct Professor in the Department of Mathematics and Statistics at York University as well as Vice President of Models and Analytics at Manulife Financial, Canada. Dr. Xie is on the Board of Directors for the Canadian-Chinese Finance Association, and his research interests include financial engineering, mathematical finance, and partial differential equations.

• Preface xviiFinancial Glossary xxiiPart I Measure Theory1 Sets and Sequences 32 Measures 153 Extension of Measures 294 Lebesgue-Stieltjes Measures 375 Measurable Functions 476 Lebesgue Integration 577 The Radon-Nikodym Theorem 778 LP Spaces 859 Convergence 9710 Product Measures 113Part II Probability Theory11 Events and Random Variables 12712 Independence 14113 Expectation 16114 Conditional Expectation 17315 Inequalities 18916 Law of Large Numbers 19917 Characteristic Functions 21718 Discrete Distributions 22719 Continuous Distributions 23920 Central Limit Theorems 257Part III Stochastic Processes21 Stochastic Processes 27122 Martingales 29123 Stopping Times 30124 Martingale Inequalities 32125 Martingale Convergence Theorems 33326 Random Walks 34327 Poisson Processes 35728 Brownian Motion 37329 Markov Processes 38930 Lévy Processes 401Part IV Stochastic Calculus31 The Wiener Integral 42132 The Itô Integral 43133 Extension of the Itô Integral 45334 Martingale Stochastic Integrals 46335 The Itô Formula 47736 Martingale Representation Theorem 49537 Change of Measure 50338 Stochastic Differential Equations 51539 Diffusion 53140 The Feynman-Kac Formula 547Part V Stochastic Financial Models41 Discrete-Time Models 56142 Black-Scholes Option Pricing Models 57943 Path-Dependent Options 59344 American Options 60945 Short Rate Models 62946 Instantaneous Forward Rate Models 64747 LIBOR Market Models 667References 687List of Symbols 703Subject Index 707