Martingales and Financial Mathematics in Discrete Time. Benoîte de Saporta

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      1  Cover

      2  Title Page

      3  Copyright

      4  Preface

      5  Introduction

      6  1 Elementary Probabilities and an Introduction to Stochastic Processes 1.1. Measures and σ-algebras 1.2. Probability elements 1.3. Stochastic processes 1.4. Exercises

      7  2 Conditional Expectation 2.1. Conditional probability with respect to an event 2.2. Conditional expectation 2.3. Geometric interpretation 2.4. Conditional expectation and independence 2.5. Exercises

      8  3 Random Walks 3.1. Trajectories of the random walk 3.2. Asymptotic behavior 3.3. The Gambler’s ruin 3.4. Exercises

      9  4 Martingales 4.1. Definition 4.2. Martingale transform 4.3. The Doob decomposition 4.4. Stopping time 4.5. Stopped martingales 4.6. Exercises

      10  5 Financial Markets 5.1. Financial assets 5.2. Investment strategies 5.3. Arbitrage 5.4. The Cox, Ross and Rubinstein model 5.5. Exercises 5.6. Practical work

      11  6 European Options 6.1. Definition 6.2. Complete markets 6.3. Valuation and hedging 6.4. Cox, Ross and Rubinstein model 6.5. Exercises 6.6. Practical work: Simulating the value of a call option

      12  7 American Options 7.1. Definition 7.2. Optimal stopping 7.3. Application to American options 7.4. The Cox, Ross and Rubinstein model 7.5. Exercises 7.6. Practical work

      13  8 Solutions to Exercises and Practical Work 8.1. Solutions to exercises in Chapter 1 8.2. Solutions to exercises in Chapter 2 8.3. Solutions to exercises in Chapter 3 8.4. Solutions to exercises in Chapter 4 8.5. Solutions to exercises in Chapter 5 8.6. Solutions to the practical exercises in Chapter 5 8.7. Solutions to exercises in Chapter 6 8.8. Solution to the practical exercise in Chapter 6 (section 6.6) 8.9. Solution to exercises in Chapter 7 8.10. Solution to the practical exercise in Chapter 7 (section 7.6)

      14  References

      15  Index

      16  End User License Agreement

      1 Chapter 3Figure 3.1. Graphical representation of a trajectory of a random walk between 0 ...Figure 3.2. Two paths from (1, 1) to (5, 3). For a color version of this figure,...Figure 3.3. A path from (0, 2) to (11, 1) passing through 0 (the unbroken blue l...

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