Risk and Financial Management: Mathematical and Computational Methods.
BY C. Tapiero
2004 John Wiley & Sons, Ltd
ISBN: 0-470-84908-8

Contents
Preface xiii
Part I: Finance and Risk Management
Chapter 1 Potpourri 03
1.1 Introduction 03
1.2 Theoretical finance and decision making 05
1.3 Insurance and actuarial science 07
1.4 Uncertainty and risk in finance 10
1.4.1 Foreign exchange risk 10
1.4.2 Currency risk 12
1.4.3 Credit risk 12
1.4.4 Other risks 13
1.5 Financial physics 15
Selected introductory reading 16
Chapter 2 Making Economic Decisions under Uncertainty 19
2.1 Decision makers and rationality 19
2.1.1 The principles of rationality and bounded rationality 20
2.2 Bayes decision making 22
2.2.1 Risk management 23
2.3 Decision criteria 26
2.3.1 The expected value (or Bayes) criterion 26
2.3.2 Principle of (Laplace) insufficient reason 27
2.3.3 The minimax (maximin) criterion 28
2.3.4 The maximax (minimin) criterion 28
2.3.5 The minimax regret or Savage’s regret criterion 28
2.4 Decision tables and scenario analysis 31
2.4.1 The opportunity loss table 32
2.5 EMV, EOL, EPPI, EVPI 33
2.5.1 The deterministic analysis 34
2.5.2 The probabilistic analysis 34
Selected references and readings 38
Chapter 3 Expected Utility 39
3.1 The concept of utility 39
3.1.1 Lotteries and utility functions 40
3.2 Utility and risk behaviour 42
3.2.1 Risk aversion 43
3.2.2 Expected utility bounds 45
3.2.3 Some utility functions 46
3.2.4 Risk sharing 47
3.3 Insurance, risk management and expected utility 48
3.3.1 Insurance and premium payments 48
3.4 Critiques of expected utility theory 51
3.4.1 Bernoulli, Buffon, Cramer and Feller 51
3.4.2 Allais Paradox 52
3.5 Expected utility and finance 53
3.5.1 Traditional valuation 54
3.5.2 Individual investment and consumption 57
3.5.3 Investment and the CAPM 59
3.5.4 Portfolio and utility maximization in practice 61
3.5.5 Capital markets and the CAPM again 63
3.5.6 Stochastic discount factor, assets pricing
and the Euler equation 65
3.6 Information asymmetry 67
3.6.1 ‘The lemon phenomenon’ or adverse selection 68
3.6.2 ‘The moral hazard problem’ 69
3.6.3 Examples of moral hazard 70
3.6.4 Signalling and screening 72
3.6.5 The principal–agent problem 73
References and further reading 75
Chapter 4 Probability and Finance 79
4.1 Introduction 79
4.2 Uncertainty, games of chance and martingales 81
4.3 Uncertainty, random walks and stochastic processes 84
4.3.1 The random walk 84
4.3.2 Properties of stochastic processes 91
4.4 Stochastic calculus 92
4.4.1 Ito’s Lemma 93
4.5 Applications of Ito’s Lemma 94
4.5.1 Applications 94
4.5.2 Time discretization of continuous-time
finance models 96
4.5.3 The Girsanov Theorem and martingales∗ 104
References and further reading 108
Chapter 5 Derivatives Finance 111
5.1 Equilibrium valuation and rational expectations 111