Stochastic methods in economics and finance

Title......Page 3
Copyright Page......Page 4
Contents......Page 6
Foreword......Page 9
Preface......Page 11
Acknowledgments......Page 14
2. Probability spaces......Page 16
3. Random variables......Page 19
4. Expectation......Page 23
5. Conditional probability......Page 27
6. Martingales and applications......Page 31
7. Stochastic processes......Page 47
8. Optimal stopping......Page 58
9. Miscellaneous applications and exercises......Page 72
10. Further remarks and references......Page 75
2. Modeling uncertainty......Page 80
3. Stochastic integration......Page 84
4. Ito\'s lemma......Page 95
5. Examples......Page 104
6. Stochastic differential equations......Page 107
7. Properties of solutions......Page 111
8. Point equilibrium and stability......Page 117
9. Existence of stationary distribution......Page 121
10. Stochastic control......Page 123
11. Bismut\'s approach......Page 133
12. Jump processes......Page 136
13. Optimal stopping and free boundary problems......Page 139
14. Miscellaneous applications and exercises......Page 143
15. Further remarks and references......Page 147
2. Neoclassical economic growth under uncertainty......Page 156
3. Growth in an open economy under uncertainty......Page 158
4. Growth under uncertainty: Properties of solutions......Page 159
5. Growth under uncertainty: Stationary distribution......Page 161
6. The stochastic Ramsey problem......Page 163
7. Bismut on optimal growth......Page 165
8. The rational expectations hypothesis......Page 168
9. Investment under uncertainty......Page 172
*10. Competitive processes, transversality condition and convergence......Page 176
*11. Rational expectations equilibrium......Page 183
12. Linear quadratic objective function......Page 187
13. State valuation functions of exponential form......Page 188
14. Money, prices and inflation......Page 193
*15. An N-sector discrete growth model......Page 197
16. Competitive firm under price uncertainty......Page 203
17. Stabilization in the presence of stochastic disturbances......Page 207
18. Stochastic capital theory in continuous time......Page 209
19. Miscellaneous applications and exercises......Page 220
20. Further remarks and references......Page 229
2. Stochastic rate of inflation......Page 232
3. The Black-Scholes option pricing model......Page 235
4. Consumption and portfolio rules......Page 238
5. Hyperbolic absolute risk aversion functions......Page 241
6. Portfolio jump processes......Page 243
7. The demand for index bonds......Page 245
8. Term structure in an efficient market......Page 248
9. Market risk adjustment in project valuation......Page 251
10. Demand for cash balances......Page 253
*11. The price of systematic risk......Page 257
*12. An asset pricing model......Page 261
*13. Existence of an asset pricing function......Page 269
*14. Certainty equivalence formulae......Page 271
*15. A testable formula......Page 277
*16. An example......Page 279
17. Miscellaneous applications and exercises......Page 283
18. Further remarks and references......Page 287
Selected bibliography......Page 294
Author index......Page 310
Subject index......Page 314