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Basic Notation1 Preliminaries from Probability Theory 1.1 Discrete Random Variables and Distributions 1.2 Continuous Random Variables and Distributions 1.3 Moments of Random Variables 1.4 Joint Distributions and Random Vectors 1.5 Copulas (*) 1.6 Exercises for Chapter 12 Statistical Methods 2.1 Limit Theorems 2.2 Confidence Intervals 2.3 Estimation Methods 2.4 Maximum Likelihood Estimation 2.5 Normal Variance Mixture Models 2.6 Distribution of Index Log-Returns 2.7 Convergence of Random Sequences 2.8 Exercises for Chapter 23 Modeling via Stochastic Processes 3.1 Introduction to Stochastic Processes 3.2 Certain Classes of Stochastic Processes 3.3 Discrete Time Markov Chains 3.4 Continuous Time Markov Chains 3.5 Poisson Processes 3.6 Levy Processes (*) 3.7 Insurance Risk Modeling (*) 3.8 Exercises for Chapter 34 Diffusion Processes 4.1 Continuous Markov Processes 4.2 Examples for Continuous Markov Processes 4.3 Diffusion Processes 4.4 Kolmogorov Equations 4.5 Diffusions with Stationary Densities 4.6 Multi-Dimensional Diffusion Processes (*) 4.7 Exercises for Chapter 45 Martingales and Stochastic Integrals 5.1 Martingales 5.2 Quadratic Variation and Covariation 5.3 Gains from Trade as Stochastic Integral 5.4 It5 Integral for Wiener Processes 5.5 Stochastic Integrals for Semimartingales (*) 5.6 Exercises for Chapter 56 The It6 Formula 6.1 The Stochastic Chain Rule 6.2 Multivariate It5 Formula 6.3 Some Applications of the It5 Formula 6.4 Extensions of the It5 Formula 6.5 Levy's Theorem (*) 6.6 A Proof of the It5 Formula (*) 6.7 Exercises for Chapter 67 Stochastic Differential Equations 7.1 Solution of a Stochastic Differential Equation 7.2 Linear SDE with Additive Noise 7.3 Linear SDE with Multiplicative Noise 7.4 Vector Stochastic Differential Equations 7.5 Constructing Explicit Solutions of SDEs 7.6 Jump Diffusions (*) 7.7 Existence and Uniqueness (*) 7.8 Markovian Solutions of SDEs (*) 7.9 Exercises for Chapter 78 Introduction to Option Pricing 8.1 Options 8.2 Options under the Black-Scholes Model 8.3 The Black-Scholes Formula 8.4 Sensitivities for European Call Option 8.5 European Put Option 8.6 Hedge Simulation 8.7 Squared Bessel Processes (*) 8.8 Exercises for Chapter 89 Various Approaches to Asset Pricing 9.1 Real World Pricing 9.2 Actuarial Pricing 9.3 Capital Asset Pricing Model 9.4 Risk Neutral Pricing 9.5 Girsanov Transformation and Bayes Rule (*) 9.6 Change of Numeraire (*) 9.7 Feynman-Kac Formula (*) 9.8 Exercises for Chapter 910 Continuous Financial Markets 10.1 Primary Security Accounts and Portfolios 10.2 Growth Optimal Portfolio 10.3 Supermartingale Property 10.4 Real World Pricing 10.5 GOP as Best Performing Portfolio 10.6 Diversified Portfolios in CFMs 10.7 Exercises for Chapter 1011 Portfolio Optimization 11.1 Locally Optimal Portfolios 11.2 Market Portfolio and GOP 11.3 Expected Utility Maximization 11.4 Pricing Nonreplicable Payoffs 11.5 Hedging 11.6 Exercises for Chapter 1112 Modeling Stochastic Volatility 12.1 Stochastic Volatility 12.2 Modified CEV Model 12.3 Local Volatility Models 12.4 Stochastic Volatility Models 12.5 Exercises for Chapter 1213 Minimal Market Model 13.1 Parametrization via Volatility or Drift 13.2 Stylized Minimal Market Model 13.3 Derivatives under the MMM 13.4 MMM with Random Scaling (*) 13.5 Exercises for Chapter 1314 Markets with Event Risk 14.1 Jump Diffusion Markets 14.2 Diversified Portfolios 14.3 Mean-Variance Portfolio Optimization 14.4 Real World Pricing for Two Market Models 14.5 Exercises for Chapter 1415 Numerical Methods 15.1 Random Number Generation 15.2 Scenario Simulation 15.3 Classical Monte Carlo Method 15.4 Monte Carlo Simulation for SDEs 15.5 Variance Reduction of Functionals of SDE 15.6 Tree Methods 15.7 Finite Difference Methods 15.8 Exercises for Chapter 1516 Solutions for Exercises AcknowledgementsReferencesAuthor IndexIndex