Robert C. Merton--Continuous Time Finance

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Contents
I Introduction to Finance and the Mathematics of Continuous-Time Models xv
1 Modern Finance 1
2 Introduction to Portfolio Selection and Capital Market Theory: Static
Analysis 13
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 One-Period Portfolio Selection . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Risk Measures for Securities and Portfolios in the One-Period Model 20
2.4 Spanning, Separation, and Mutual-Fund Theorems . . . . . . . . . . . 26
3 On the Mathematics and Economics Assumptions of Continuous-Time
Models 45
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2 Continuous-Sample-Path Processes with “No Rare Events” . . . . . . 52
3.3 Continuous-Sample-Path Processes with “Rare Events” . . . . . . . . 64
3.4 Discontinuous-Sample-Path Processes with “Rare Events” . . . . . . 68
II Optimum Consumption and Portfolio Selection in Continuous-Time Models 75
4 Lifetime Portfolio Selection Under Uncertainty: The Continuous-Time
Case 76
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.2 Dynamics of the Model: The Budget Equation . . . . . . . . . . . . . 76
4.3 The Two-Asset Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.4 Constant Relative Risk Aversion . . . . . . . . . . . . . . . . . . . . . 81
4.5 Dynamic Behavior and the Bequest Valuation Function . . . . . . . . 83
4.6 In?nite Time Horizon . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.7 Economic Interpretation of the Optimal Decision Rules for Portfolio
Selection and Consumption . . . . . . . . . . . . . . . . . . . . . . . . 86
4.8 Extension to Many Assets . . . . . . . . . . . . . . . . . . . . . . . . 90
4.9 Constant Absolute Risk Aversion . . . . . . . . . . . . . . . . . . . . 91
4.10 Other Extensions of the Model . . . . . . . . . . . . . . . . . . . . . . 92
5 Optimum Consumption and Portfolio Rules in a Continuous-timeModel 94
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.2 A Digression on It ? o Processes . . . . . . . . . . . . . . . . . . . . . . 95
5.3 Asset-Price Dynamics and the Budget Equation . . . . . . . . . . . . 97
5.4 Optimal Portfolio and Consumption Rules: The Equations of Opti-
mality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.5 Log-Normality of Prices and the Continuous-Time Analog to Tobin-
Markowitz Mean-Variance Analysis . . . . . . . . . . . . . . . . . . . 103
5.6 Explicit Solutions for a Particular Class of Utility Functions . . . . . 107
5.7 Noncapital Gains Income: Wages . . . . . . . . . . . . . . . . . . . . 111
5.8 Poisson Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.9 Alternative Price Expectations to the Geometric Brownian Motion . . 117
5.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6 Further Developments in the Theory of Optimal Consumption and Port-
folio Selection 128
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.2 The Cox-Huang Alternative to Stochastic Dynamic Programming . . 130
6.2.1 The Growth-Optimum Portfolio Strategy . . . . . . . . . . . . 130
6.2.2 The Cox-Huang Solution of the Intertemporal Consumption-
Investment Problem . . . . . . . . . . . . . . . . . . . . . . . 133
6.2.3 The Relation Between the Cox-Huang and Dynamic Pro-
gramming Solutions . . . . . . . . . . . . . . . . . . . . . . . 139
6.3 Optimal Portfolio Rules when the Nonnegativity Constraint on Con-
sumption is Binding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
6.4 Generalized Preferences and Their Impact on Optimal Portfolio De-
mands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
III Warrant and Option Pricing Theory 165
7 A Complete Model of Warrant Pricing that Maximizes Utility 166
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
7.2 Cash-Stock Portfolio Analysis . . . . . . . . . . . . . . . . . . . . . . 166
7.3 Recapitulation of the 1965 Model . . . . . . . . . . . . . . . . . . . . 170
7.4 Determining Average Stock Yield . . . . . . . . . . . . . . . . . . . . 172
7.5 Determining Warrant Holdings and Prices . . . . . . . . . . . . . . . . 173
7.6 Digression: General Equilibrium Pricing . . . . . . . . . . . . . . . . 175
7.7 Utility-Maximizing Warrant Pricing: The Important “Incipient” Case 176
7.8 Explicit Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
7.9 Warrants Never to be Converted . . . . . . . . . . . . . . . . . . . . . 180
7.10 Exact Solution to the Perpetual Warrant Case . . . . . . . . . . . . . . 182
7.11 Illustrative Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
7.12 Proof of the Superiority of Yield ofWarrants Over Yield of Common
Stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
7.13 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
8 Theory of rational option pricing 196
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
8.2 Restrictions on Rational Option Pricing . . . . . . . . . . . . . . . . . 197
8.3 Effects of Dividends and Changing Exercise Price . . . . . . . . . . . 207
8.4 Restrictions on Rational Put Option Pricing . . . . . . . . . . . . . . . 213
8.5 Rational Option Pricing Along Black-Scholes Lines . . . . . . . . . . 216
8.6 An Alternative Derivation of the Black-Scholes Model . . . . . . . . 218
8.7 Extension of the Model to Include Dividend Payments And Exercise
Price Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
8.8 Valuing an American Put Option . . . . . . . . . . . . . . . . . . . . . 230
8.9 Valuing the “Down-and-Out” Call Option . . . . . . . . . . . . . . . . 232
8.10 Valuing a Callable Warrant . . . . . . . . . . . . . . . . . . . . . . . . 234
8.11 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
9 Option Pricing When Underlying Stock Returns are Discontinuous 239
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
9.2 The Stock Price and Option Price Dynamics . . . . . . . . . . . . . . 241
9.3 An Option Pricing Formula . . . . . . . . . . . . . . . . . . . . . . . . 246
9.4 A Possible Answer to an Empirical Puzzle . . . . . . . . . . . . . . . 251
10 Further Developments in Option Pricing Theory 256
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
10.2 Cox-Ross “Risk-Neutral” Pricing and the Binomial Option Pricing
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
10.3 Pricing Options on Futures Contracts . . . . . . . . . . . . . . . . . . 270
IV Contingent-Claims Analysis in the Theory of Corporate Finance and Finan-
cial Intermediation 277
11 A Dynamic General Equilibrium Model of the Asset Market and Its Ap-
plication to the Pricing of the Capital Structure of the Firm 278
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
11.2 A Partial-Equilibrium One-Period Model . . . . . . . . . . . . . . . . 278
11.3 Some Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
11.4 A General Intertemporal Equilibrium Model of the Asset Market . . . 286
11.5 Model I: A Constant Interest Rate Assumption . . . . . . . . . . . . . 291
11.6 Model II: The “No Riskless Asset” Case . . . . . . . . . . . . . . . . 296
11.7 Model III: The General Model . . . . . . . . . . . . . . . . . . . . . . 297

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关键词：Continuous Finance Robert Financ Merton Robert

11.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
12 On the Pricing of Corporate Debt: The Risk Structure of Interest Rates 303
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
12.2 On The Pricing of Corporate Liabilities . . . . . . . . . . . . . . . . . 304
12.3 On Pricing “Risky” Discount Bonds . . . . . . . . . . . . . . . . . . . 307
12.4 A Comparative Statics Analysis of the Risk Structure . . . . . . . . . 309
12.5 On the Modigliani-Miller Theorem with Bankruptcy . . . . . . . . . . 317
12.6 On the Pricing of Risky Coupon Bonds . . . . . . . . . . . . . . . . . 320
12.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
13 On the Pricing of Contingent Claims and theModigliani-Miller Theorem323
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
13.2 A general derivation of a contingent claim price . . . . . . . . . . . . 324
13.3 On the Modigliani-Miller Theorem with Bankruptcy . . . . . . . . . . 328
13.4 Applications of Contingent-Claims Analysis in Corporate Finance . . 331
14 Financial Intermediation in the Continuous-Time Model 337
14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
14.2 Derivative-Security Pricing with Transactions Costs . . . . . . . . . . 341
14.3 Production Theory for Zero-Transaction-Cost Financial Intermediaries 347
14.4 Risk Management for Financial Intermediaries . . . . . . . . . . . . . 354
14.5 On the Role of Efficient Financial Intermediation in the Continuous-
Time Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
14.6 Afterword: Policy and Strategy in Financial Intermediation . . . . . . 368
V An Intertemporal Equilibrium Theory of Finance 373
15 An Intertemporal Capital Asset Pricing Model 374
15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
15.2 Capital Market Structure . . . . . . . . . . . . . . . . . . . . . . . . . 376
15.3 Asset Value and Rate of Return Dynamics . . . . . . . . . . . . . . . 377
15.4 Preference Structure and Budget Equation Dynamics . . . . . . . . . 381
15.5 The Equations of Optimality: The Demand Functions for Assets . . . 382
15.6 Constant Investment Opportunity Set . . . . . . . . . . . . . . . . . . 385
15.7 Generalized Separation: A Three-Fund Theorem . . . . . . . . . . . . 386
15.8 The Equilibrium Yield Relationship among Assets . . . . . . . . . . . 388
15.9 Empirical Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391
15.10An (m + 2)-Fund Theorem and the Security Market Hyperplane . . . 393
15.11The Consumption-Based Capital Asset Pricing Model . . . . . . . . . 403
15.12Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409
16 A Complete-Markets General Equilibrium Theory of Finance in Contin-
uous Time 413
16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
16.2 Financial Intermediation with Dynamically-Complete Markets . . . . 416
16.3 Optimal Consumption and Portfolio Rules with Dynamically-Complete
Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424
16.4 General Equilibrium: The Case of Pure Exchange . . . . . . . . . . . 432
16.5 General Equilibrium: The Case of Production . . . . . . . . . . . . . 437
16.6 A General Equilibrium Model in which the Capital Asset Pricing
Model Obtains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
16.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453
VI Applications of the Continuous-Time Model to Selected Issues in Public Fi-
nance: Long-Run Economic Growth, Public Pension Plans, Deposit Insurance,
Loan Guarantees, and Endowment Management for Universities 455
17 An Asymptotic Theory of Growth Under Uncertainty 456
17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
17.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457
17.3 The Steady-State Distribution for k . . . . . . . . . . . . . . . . . . . 461
17.4 The Cobb-Douglas/Constant Savings Function Economy . . . . . . . 462
17.5 The Stochastic Ramsey Problem . . . . . . . . . . . . . . . . . . . . . 466
18 On Consumption-Indexed Public Pension Plans 477
18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477
18.2 A Simple Intertemporal Equilibrium Model . . . . . . . . . . . . . . . 480
18.3 On the Merits and Feasibility of a Consumption-Indexed Public Plan . 486
19 An Analytic Derivation of the Cost of Loan Guarantees and Deposit In-
surance: An Application of Modern Option Pricing Theory 493
19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493
19.2 A model for pricing deposit insurance . . . . . . . . . . . . . . . . . . 495
20 On the Cost of Deposit Insurance When There are Surveillance Costs 501
20.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
20.2 Assumptions of the Model . . . . . . . . . . . . . . . . . . . . . . . . 502
20.3 The Evaluation of FDIC Liabilities . . . . . . . . . . . . . . . . . . . 503
20.4 The Evaluation of Bank Equity . . . . . . . . . . . . . . . . . . . . . . 508
20.5 On the Equilibrium Deposit Rate . . . . . . . . . . . . . . . . . . . . . 509
20.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
21 Optimal Investment Strategies for University Endowment Funds 513
21.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513
21.2 Overview of Basic Insights and Prescriptions for Policy . . . . . . . . 514
21.3 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520
21.4 Optimal Endowment Management with Other Sources of Income . . 526

大师级经典作品，数学达人可以欣赏美丽的风景。

很難很難非常南

汗，能看懂不是啥达人哈。这本挺简单的，跟DUFFIE的动态资产定价相对。。。

不错啊 多谢分享

不错啊 多谢分享

好书，顶lz

one more top-notch classical must-to-download, thanx man

这是一本非常经典的书