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Stochastic Finance: An Introduction with Examples [Pehme köide]

(University of Leeds), (Lancaster University)
  • Formaat: Paperback / softback, 260 pages, kõrgus x laius x paksus: 247x189x13 mm, kaal: 570 g, Worked examples or Exercises
  • Ilmumisaeg: 09-Feb-2023
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1009048945
  • ISBN-13: 9781009048941
Teised raamatud teemal:
Stochastic Finance: An Introduction with ExamplesSuurem pilt
  • Formaat: Paperback / softback, 260 pages, kõrgus x laius x paksus: 247x189x13 mm, kaal: 570 g, Worked examples or Exercises
  • Ilmumisaeg: 09-Feb-2023
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1009048945
  • ISBN-13: 9781009048941
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781009048941.html
Märksõnad:
A relaxed and user-friendly introduction to financial mathematics for advanced undergraduate mathematics students. This is core material for students of financial mathematics, and fundamental for anyone planning a career in the field.

Stochastic Finance provides an introduction to mathematical finance that is unparalleled in its accessibility. Through classroom testing, the authors have identified common pain points for students, and their approach takes great care to help the reader to overcome these difficulties and to foster understanding where comparable texts often do not. Written for advanced undergraduate students, and making use of numerous detailed examples to illustrate key concepts, this text provides all the mathematical foundations necessary to model transactions in the world of finance. A first course in probability is the only necessary background. The book begins with the discrete binomial model and the finite market model, followed by the continuous Black–Scholes model. It studies the pricing of European options by combining financial concepts such as arbitrage and self-financing trading strategies with probabilistic tools such as sigma algebras, martingales and stochastic integration. All these concepts are introduced in a relaxed and user-friendly fashion.

Arvustused

'The text does a great job of providing a comprehensive picture of basic mathematical finance concepts in both discrete and continuous settings. The authors provide a balanced amount of details in both the financial (arbitrage, replicating strategies, etc.) and mathematical aspects (probability, stochastic calculus, etc.) I really appreciate the fact that the technical details are presented in a way that is accessible to an advanced undergraduate student.' Triet Pham, Department of Mathematics, The School of Arts and Sciences, Rutgers, The State University of New Jersey 'This is a rigorous textbook on stochastic finance in which the reader will enjoy the path the authors take while introducing conditional expectations with respect to sigma-algebras, and the sequence of models from the binomial to Black-Scholes. In all, a careful construction of the theory with proofs that are both thorough and readable.' Ludolf E. Meester, Delft University of Technology

Muu info

A relaxed and user-friendly approach to understanding financial mathematics and the pricing of options with extensive examples and exercises.
Preface ix
Acknowledgements x
Part I Discrete-Time Models for Finance
1 Introduction to Finance
3(14)
1.1 Motivation
3(1)
1.2 Financial Markets
4(5)
1.2.1 Primary Markets
4(1)
1.2.2 Secondary Markets
5(2)
1.2.3 Payoffs
7(2)
1.2.4 Payoff Diagrams
9(1)
1.3 Arbitrage Opportunities and Liquid Markets
9(6)
1.4 Exercises
15(2)
2 Discrete Probability
17(45)
2.1 Basics
17(5)
2.2 Conditional Expectation
22(17)
2.2.1 Conditioning on an Event B
22(4)
2.2.2 Conditioning on Partitions and Random Variables
26(7)
2.2.3 Properties of Conditional Expectation
33(6)
2.3 Modelling the Information Available in the Future
39(20)
2.3.1 Motivation
40(1)
2.3.2 Definition of a a-Algebra
41(3)
2.3.3 Visualisation of ct-Algebras
44(3)
2.3.4 er-Algebras Generated by Random Variables
47(6)
2.3.5 Measurable Random Variables and Conditioning
53(6)
2.4 Exercises
59(3)
3 Binomial or CRR Model
62(35)
3.1 Model Specification
62(2)
3.2 Trading Strategies
64(5)
3.3 Pricing of European Contingent Claims
69(24)
3.3.1 One Period (T= 1)
72(8)
3.3.2 Multi-period Case (T Arbitrary)
80(13)
3.4 American Contingent Claims
93(2)
3.5 Exercises
95(2)
4 Finite Market Model
97(26)
4.1 Model Specification and Notation
97(3)
4.1.1 Model Specification
97(1)
4.1.2 Trading Strategies
98(1)
4.1.3 Discounted Asset Prices
99(1)
4.2 First Fundamental Theorem of Asset Pricing
100(8)
4.3 Second Fundamental Theorem of Asset Pricing
108(5)
4.4 Pricing of Replicable European Contingent Claims
113(3)
4.5 Incomplete Markets
116(4)
4.6 Exercises
120(3)
5 Discrete Black-Scholes Model
123(16)
5.1 Heuristic Considerations on the Stock Price
123(2)
5.2 Model Specification
125(1)
5.3 Trading Strategies and Discounted Asset Prices
126(2)
5.4 Risk-Neutral Measure
128(3)
5.5 Black-Scholes Formula
131(2)
5.6 Replicating Strategies
133(2)
5.7 Exercises
135(4)
Part II Continuous-Time Models for Finance
6 Continuous Probability
139(25)
6.1 Basics
139(12)
6.1.1 General Probability Spaces
139(1)
6.1.2 Measures on an Arbitrary Probability Space
140(4)
6.1.3 Random Variables
144(3)
6.1.4 Convergence of Random Variables
147(4)
6.2 Review of Stochastic Processes
151(5)
6.3 Filtrations and Conditional Expectations
156(6)
6.4 Exercises
162(2)
7 Brownian Motion
164(12)
7.1 Definition of Brownian Motion
164(3)
7.2 Properties of Sample Paths of Brownian Motion
167(2)
7.3 Transformations of Brownian Motion
169(5)
7.4 Exercises
174(2)
8 Stochastic Integration
176(34)
8.1 The Riemann Integral
176(3)
8.2 The Riemann-Stieltjes Integral
179(4)
8.3 Quadratic Variation
183(3)
8.4 Construction of the Stochastic Integral
186(9)
8.5 Properties of the Stochastic Integral
195(3)
8.6 Ito's Formula
198(7)
8.7 Stochastic Differential Equations
205(3)
8.8 Exercises
208(2)
9 The Black-Scholes Model
210(28)
9.1 Model Specification
210(1)
9.2 Trading Strategies
211(7)
9.3 Arbitrage and Risk-Neutral Measure
218(7)
9.4 Black-Scholes Formula
225(4)
9.5 The Black-Scholes Greeks
229(3)
9.5.1 Volatility
231(1)
9.6 Terminal Value Claims
232(4)
9.7 Exercises
236(2)
Appendix A Supplementary Material
238(10)
A.1 Elementary Limit Theorems
238(2)
A.2 Measures on Countable Sample Spaces
240(1)
A.3 Discontinuities of Cadlag Functions
241(1)
A.4 Omitted Proofs
242(6)
Bibliography 248(1)
Symbol Index 249(2)
Index 251
Amanda Turner is Professor of Statistics at the University of Leeds. She received her Ph.D. from the University of Cambridge in Scaling Limits of Stochastic Processes in 2007. Before moving to Leeds, she taught probability and stochastic processes for finance at Lancaster University and the University of Geneva for over fifteen years. She is a founding member of the Royal Statistical Society's Applied Probability Section and is heavily involved in the London Mathematical Society, including as a member of council since 2021. When not doing mathematics, she enjoys mountaineering and skiing. Dirk Zeindler is Senior Lecturer in Pure Mathematics at Lancaster University. He holds a Ph.D. in random matrix theory from the University of Zurich. He has taught probability courses at Lancaster University and at the University of Bielefeld for over ten years. His teaching includes introductory first-year probability to advanced financial mathematics, for mathematics, accounting and finance students. His research interests are in probability and number theory. In particular, he and his co-authors have proven that at least 41.7% of the zeros of the Riemann zeta lie on the critical line, which is the current world record.