Continuous-Time Models in Corporate Finance, Banking, and Insurance

Cover......Page 1
Title......Page 4
Copyright......Page 5
Dedication......Page 6
Contents......Page 8
Preface......Page 12
Introduction......Page 16
1.1 Modeling assumptions......Page 22
1.2 Pricing corporate debt......Page 24
1.3.1 The general form of the valuation equation......Page 26
1.3.2 The price of a consol bond......Page 28
1.4 Dynamic trade-off theory......Page 30
1.4.2 Asset pricing......Page 31
1.4.3 Financial decisions......Page 34
1.4.4 Testable predictions......Page 36
1.5 Further reading......Page 37
2.1 The dynamics of net earnings......Page 41
2.2 Risk-averse shareholders......Page 42
2.2.1 Shareholder value......Page 43
2.2.2 The optimal dividend flow......Page 45
2.2.3 The value function......Page 46
2.3 Risk-neutral shareholders......Page 48
2.3.1 The dynamics of liquid reserves and the value function......Page 49
2.3.2 The optimal dividend-distribution strategy......Page 53
2.3.3 Economic implications......Page 56
2.4 Further reading......Page 57
3.1 Fixed issuance cost and stock-price dynamics......Page 60
3.1.1 Optimal equity issuance with a fixed issuance cost......Page 61
3.1.2 The impact of equity-issuance on the value function......Page 63
3.1.3 When is equity issuance too costly?......Page 65
3.1.4 Stock-price dynamics......Page 66
3.2 Proportional issuance cost......Page 68
3.2.2 Characterizing the optimal dividend-distribution barrier......Page 69
3.2.3 The optimal equity-issuance strategy when the issuance cost is proportional......Page 71
3.3.1 The cash-reserves dynamics with uncertain refinancing......Page 72
3.3.2 The amount of uncertain refinancing......Page 73
3.3.3 The refinancing region and the target cash level......Page 75
3.4 Further reading......Page 76
4.1.1 The model......Page 78
4.1.2 The impact of a minimum-capital requirement......Page 79
4.1.3 A minimum-capital requirement with recapitalization......Page 81
4.2 A bank's portfolio problem......Page 82
4.2.1 Setting up the stochastic-control problem......Page 83
4.2.2 The value function and the first-best......Page 84
4.3.1 The model......Page 89
4.3.2 The optimal funding strategies......Page 92
4.3.3 Numerical analysis......Page 95
4.4 Further reading......Page 96
5.1 The base liquidity-management model with large losses......Page 99
5.1.2 The value function......Page 100
5.1.3 Computing the value function......Page 103
5.2 Reinsuring Brownian risks......Page 104
5.2.1 The dynamics of liquid reserves and the variational inequality......Page 105
5.2.2 The partial-exposure region......Page 106
5.2.3 The full-exposure region......Page 108
5.2.4 Sensitivity analysis......Page 109
5.3.1 The cash-reserves dynamics......Page 111
5.3.2 The optimal reinsurance strategy......Page 112
5.4 Further reading......Page 113
6.1 The "q-model" of corporate investment......Page 116
6.1.1 The stock of capital and its productivity......Page 117
6.1.3 Tobin's q......Page 118
6.2 Introducing external financial frictions......Page 120
6.2.1 The impact of liquidity constraints on firm value......Page 121
6.2.2 The size-adjusted value function......Page 122
6.2.3 Optimal investment and Tobin's q......Page 124
6.3.1 The model......Page 125
6.3.2 The interaction between investment and dividend payouts......Page 126
6.3.3 The optimal investment time......Page 128
6.4 Further reading......Page 130
7.1 Asset substitution and capital structure......Page 132
7.1.1 The model......Page 133
7.1.2 The risk-shifting problem......Page 134
7.1.3 The impact of risk shifting on firm value......Page 135
7.2.1 The model......Page 136
7.2.2 The manager's continuation utility......Page 138
7.2.3 The principal's value function and the optimal contract......Page 139
7.2.4 Implementing the optimal contract through the firm's capital structure......Page 142
7.3.1 The model......Page 145
7.3.2 The contracting problem......Page 146
7.3.3 Addressing incentive compatibility......Page 147
7.3.4 The financiers' value function......Page 148
7.3.5 The size-adjusted problem and the optimal contract......Page 150
7.4 Further reading......Page 152
8.1.1 The model......Page 155
8.1.2 The value function of a financial intermediary......Page 157
8.1.3 The value function of households and the competitive equilibrium......Page 159
8.2.1 The model......Page 161
8.2.2 Equilibrium......Page 164
8.2.3 The long-term behavior of the economy......Page 165
8.3 Insurance cycles......Page 167
8.3.1 The model......Page 168
8.3.2 Equilibrium......Page 170
8.3.3 Dynamics of insurance prices......Page 175
8.4 Further reading......Page 176
A.1 Chapter 1......Page 178
A.2 Chapter 2......Page 179
A.3 Chapter 3......Page 184
A.4 Chapter 4......Page 188
A.5 Chapter 5......Page 193
A.6 Chapter 7......Page 195
A.7 Chapter 8......Page 198
Appendix B The Modigliani-Miller Theorem......Page 200
C.1 Filtrations, Martingales and Itô Processes......Page 203
C.2 The Itô Formula......Page 207
C.3 The Martingale Representation Theorem(s)......Page 210
C.4 The Optimal Sampling Theorem......Page 211
References......Page 213
Index......Page 222