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El. knyga: Physics and Finance

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Physics and FinanceDidesnis paveikslėlis
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This book introduces physics students to concepts and methods of finance. Despite being perceived as quite distant from physics, finance shares a number of common methods and ideas, usually related to noise and uncertainties. Juxtaposing the key methods to applications in both physics and finance articulates both differences and common features, this gives students a deeper understanding of the underlying ideas. Moreover, they acquire a number of useful mathematical and computational tools, such as stochastic differential equations, path integrals, Monte-Carlo methods, and basic cryptology. Each chapter ends with a set of carefully designed exercises enabling readers to test their comprehension.


1 Introduction
1(4)
References
3(2)
2 Concepts of Finance
5(10)
2.1 Stocks and Other Tradeable Goods
5(1)
2.2 Hedging and Shorting
6(1)
2.3 Derivatives
6(2)
2.4 Money
8(1)
2.5 Discounting and Liquidity
9(1)
2.6 Efficient Market Hypothesis
10(1)
2.7 Theoretical Markets
10(1)
2.8 Market Participants
11(4)
Exercises
13(2)
3 Portfolio Theory and CAPM
15(14)
3.1 Variational Calculus and Lagrange Multipliers
16(2)
3.2 Portfolio with Risky Assets Only
18(3)
3.3 Portfolio with a Risk-Free Asset
21(1)
3.4 Capital Market Line and Sharpe Ratio
22(2)
3.5 Capital Asset Pricing Model
24(2)
3.6 Valuation
26(3)
Exercises
27(1)
References
28(1)
4 Stochastic Processes
29(18)
4.1 Binomial Trees
29(3)
4.2 Wiener Process
32(1)
4.3 Diffusion Processes and Green's Functions
33(3)
4.4 Stochastic Integrals and Ito's Lemma
36(1)
4.5 Master and Fokker-Planck Equations
37(3)
4.6 A First Look at Option Pricing
40(4)
4.7 Digression on Expectation Values
44(3)
Exercises
45(1)
References
46(1)
5 Black-Scholes Differential Equation
47(12)
5.1 Derivation
47(2)
5.2 The Solution
49(3)
5.3 Risk-Neutrality and Martingales
52(1)
5.4 Dynamic Hedging
53(3)
5.5 Other Examples
56(3)
Exercises
58(1)
References
58(1)
6 The Greeks and Risk Management
59(10)
6.1 The Greeks
59(3)
6.2 Volatility Smile
62(1)
6.3 Value at Risk
63(1)
6.4 Tailoring Risk to One's Desire
64(5)
Exercises
68(1)
References
68(1)
7 Regression Models and Hypothesis Testing
69(22)
7.1 Regression and Linear Fitting
70(2)
7.2 Examples
72(4)
7.3 Goodness-of-Fit R2
76(1)
7.4 Χ-Distribution
77(2)
7.5 Student's t-Distribution
79(5)
7.6 Hypothesis Testing and p-Values
84(1)
7.7 F-Test
85(3)
7.8 Parsimony
88(3)
Exercises
89(1)
References
90(1)
8 Time Series
91(22)
8.1 Trend and Seasonality
92(2)
8.2 MA, AR, and ARMA
94(2)
8.3 Auto-Covariance and Autocorrelation
96(3)
8.4 Partial Autocorrelation Function
99(2)
8.5 Determining the Model Coefficients
101(1)
8.6 Box-Jenkins
102(1)
8.7 Forecasting
103(3)
8.8 Zoo of Models
106(7)
Exercises
111(1)
References
111(2)
9 Bubbles, Crashes, Fat Tails and Levy-Stable Distributions
113(32)
9.1 Historical Bubbles and Crashes
114(2)
9.2 Bubble-Crash Mechanisms
116(1)
9.3 Behavioral Economics
117(2)
9.4 Fat-Tailed Distributions
119(1)
9.5 Power Laws
120(3)
9.6 Fractals
123(4)
9.7 Sums of Random Numbers
127(3)
9.8 Levy-Stable Distributions
130(2)
9.9 Extreme-Value Theory
132(6)
9.10 Finite-Time Divergence and Log-Periodic Oscillations
138(7)
Exercises
142(1)
References
143(2)
10 Quantum Finance and Path Integrals
145(26)
10.1 Quantum Mechanics
146(2)
10.2 Black-Scholes Hamiltonian
148(1)
10.3 Pricing Kernel
149(2)
10.4 Barrier Options
151(5)
10.5 Path Integrals in Quantum Mechanics
156(4)
10.6 Path Integrals in Finance
160(4)
10.7 Monte-Carlo Integration
164(3)
10.8 Numerical Evaluation of Path Integrals
167(4)
Exercises
170(1)
References
170(1)
11 Optimal Control Theory
171(22)
11.1 Macroeconomic Models
172(6)
11.2 Control and Feedback
178(3)
11.3 Hamiltonian Mechanics
181(1)
11.4 Hamiltonians for Optimal Control
182(2)
11.5 Donkey Revisited
184(3)
11.6 Linear Quadratic Regulators
187(2)
11.7 Controlling the Robinson-Crusoe Economy
189(4)
Exercises
191(1)
References
192(1)
12 Cryptocurrencies
193(40)
12.1 Information, Probabilities, and Codes
195(3)
12.2 Relation to the Thermodynamic Entropy
198(1)
12.3 Moving Information Through Discrete Channels
199(5)
12.4 Continuous Information Channels
204(3)
12.5 Cryptography Fundamentals
207(4)
12.6 Early Public-Key Systems
211(3)
12.7 Elliptic Curve Cryptography
214(4)
12.8 Bitcoins and Blockchains
218(3)
12.9 Ethereum and Smart Contracts
221(3)
12.10 Quantum Computing
224(9)
Exercises
230(1)
References
231(2)
13 Solutions for Selected Exercises
233(28)
Appendix A On the Independence of Certain Random Variables 261(4)
Appendix B Software 265(16)
Index 281
Volker Ziemann obtained his Ph.D. in accelerator physics from Dortmund University in 1990. After postdoctoral positions in Stanford at SLAC and in Geneva at CERN, where he worked on the design of the LHC, in 1995, he moved to Uppsala where he worked at the electron-cooler storage ring CELSIUS. In 2005, he moved to the physics department where he has since taught physics. He was responsible for several accelerator physics projects at CERN, DESY, and XFEL. In 2014, he received the Thuréus prize from the Royal Society of Sciences in Uppsala.
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