|
|
 |
| Àâòîðèçàöèÿ |
|
|
|
| Ïîèñê ïî óêàçàòåëÿì |
|
|
|
|
|
|
|
 |
|
|
|
| Pliska S.R. — Introduction to Mathematical Finance |
|
|
|
| Ïðåäìåòíûé óêàçàòåëü |
Multiperiod securities markets, martingale measures 93 97
Multiperiod securities markets, martingales 88 91 94—95 98
Multiperiod securities markets, model specifications, filtrations and stochastic processes 72—73
Multiperiod securities markets, model specifications, filtrations and stochastic processes, discounted gains processes 83
Multiperiod securities markets, model specifications, filtrations and stochastic processes, discounted price processes 83
Multiperiod securities markets, model specifications, filtrations and stochastic processes, discounted prices 83—84
Multiperiod securities markets, model specifications, filtrations and stochastic processes, discounted value processes 83
Multiperiod securities markets, model specifications, filtrations and stochastic processes, filtration 77—79
Multiperiod securities markets, model specifications, filtrations and stochastic processes, information structures 73—76
Multiperiod securities markets, model specifications, filtrations and stochastic processes, self-financing trading strategies 82—83
Multiperiod securities markets, model specifications, filtrations and stochastic processes, stochastic integrals 81
Multiperiod securities markets, model specifications, filtrations and stochastic processes, stochastic process models of security prices 77—79
Multiperiod securities markets, model specifications, filtrations and stochastic processes, trading strategies 80
Multiperiod securities markets, model specifications, filtrations and stochastic processes, value processes and gains processes 81—82
Multiperiod securities markets, reflection principle 105
Multiperiod securities markets, return and dividend processes 84—85
Multiperiod securities markets, return and dividend processes, dividend processes 87—88
Multiperiod securities markets, return and dividend processes, returns for discounted price processes 85
Multiperiod securities markets, return and dividend processes, returns for value and gains processes 85—87
Multiperiod securities markets, return and dividend processes, trading strategy 86
Multiperiod securities markets, risk neutral probability measures 93 99
Multiperiod securities markets, risky security processes 73
Multiperiod securities markets, state space 106
Multiperiod securities markets, state-price deflator 100
Multiperiod securities markets, stationary Markov chain 107
Multiperiod securities markets, submartingales 91
Multiperiod securities markets, supermartingales 91
Multiperiod securities markets, time-homogeneous Markov chain 107
Multiperiod securities markets, transition matrices 107
Mutual fund principle 50
Optimal consumption and investment problems, consumption-investment 162—173
Optimal consumption and investment problems, consumption-investment, with constraints 184—193
Optimal consumption and investment problems, maximum utility from consumption and terminal wealth 173—178
Optimal consumption and investment problems, optimal portfolios 149—162 178—184
Optimal consumption and investment problems, portfolio optimization in incomplete markets 193—199
Optimal portfolios 149—151
Optimal portfolios and viability 33—36
Optimal portfolios, arbitrage opportunities 151—152
Optimal portfolios, dynamic programming 153—156
Optimal portfolios, in incomplete markets 58—64
Optimal portfolios, martingale methods 156—162
Optimal portfolios, risk neutral computational approach 156—162
Optimal portfolios, with constraints 178—181
Optimal portfolios, with constraints, risk neutral computational approach 181—184
Optimal value process 153
Optional sampling theorem 131
options see “Bonds and interest rate derivatives” “Derivatives”
Pareto efficiency 66—68
Payer swaps 229
Payer swaptions 231—234
Portfolio management with short sales restrictions and similar constraints 52—58
Portfolio optimization in incomplete markets 193
Portfolio optimization in incomplete markets, dynamic programming 193—195
Portfolio optimization in incomplete markets, fictitious securities 196—199
Portfolio optimization in incomplete markets, Lagrange multiplier approach 195—196
Price process 2 (see also “Discounted price process”)
Put options 117
Put-call parity 117
Receiver swaps 229
Receiver swaptions 231—234
Reflection principle 105
Replicating portfolio 17
Replicating trading strategy 114—116 129
Return and dividend processes 84—88
Returns for discounted price processes 85
Returns for value and gains processes 85—87
Risk and return 28—31
Risk neutral computational approach, maximum utility from consumption and terminal wealth 175
Risk neutral computational approach, optimal consumption-investment with constraints 188—193
Risk neutral computational approach, optimal portfolios 156—162
Risk neutral computational approach, optimal portfolios, with constraints 181—184
Risk neutral computational approach, single period consumption and investment 37—40 44—46 53—58 61
Risk neutral probability measure, bonds and interest rate derivatives 201 203—205 218 224
Risk neutral probability measure, consumption-investment 168—173
Risk neutral probability measure, defined in terms of martingales 88
Risk neutral probability measure, finite horizon models 238 241
Risk neutral probability measure, futures 143
Risk neutral probability measure, infinite horizon models 243 246
Risk neutral probability measure, maximum utility from consumption and terminal wealth 174
Risk neutral probability measure, multiperiod securities markets 93 99
Risk neutral probability measure, single period consumption and investment 34 35—36 43 65 67
Risk neutral probability measure, single period securities markets 10 11—16 21—24 28
Risk neutral valuation principle, contingent claims 18 113
Risk neutral “conditional” probability measures 134
Risk premiums 29
Riskless interest rate 200
Risky price process, discounted and undiscounted 147
Risky security processes 73
Securities markets see “Complete markets” “Incomplete “Multiperiod “Single
Self-financing consumption-investment plans 163
Self-financing futures 142
Self-financing trading strategies 82—83
Separating hyperplane theorem 14 238
Simplex algorithm, linear program solving 250
Single period consumption and investment, admissible consumption-investment plans 41
Single period consumption and investment, arbitrage opportunities 34
Single period consumption and investment, attainable wealths 38
Single period consumption and investment, capital asset pricing model (CAPM) theory 49—50
Single period consumption and investment, complete markets 33—58
Single period consumption and investment, consumption investment problems 40—47
Single period consumption and investment, consumption processes 40—41
Single period consumption and investment, consumption-investment plans 40—41
Single period consumption and investment, demand functions 68
| Single period consumption and investment, equilibrium models 64—70
Single period consumption and investment, fictitious security approach 59—64
Single period consumption and investment, incomplete markets 58—64
Single period consumption and investment, marginal utility of terminal wealth 35
Single period consumption and investment, mean-variance portfolio analysis 47—51
Single period consumption and investment, mutual fund principle 50
Single period consumption and investment, optimal portfolios and viability 33—36
Single period consumption and investment, optimal portfolios in incomplete markets 58—64
Single period consumption and investment, Pareto efficiency 66—68
Single period consumption and investment, portfolio management with short sales, restrictions and similar constraints 52—58
Single period consumption and investment, risk neutral computational approach 37—40 44—46 53—58 61
Single period consumption and investment, risk neutral probability measures 34 35—36 43 65 67
Single period consumption and investment, state price density 35
Single period securities markets, arbitrage opportunities 8—10 11—13 17 24
Single period securities markets, arbitrage pricing theory 17
Single period securities markets, bank account process 1
Single period securities markets, classification 9—10
Single period securities markets, complete markets 21—24
Single period securities markets, contingent claims, attainable 17
Single period securities markets, contingent claims, complete markets 24
Single period securities markets, contingent claims, incomplete markets 24
Single period securities markets, contingent claims, marketable 17
Single period securities markets, contingent claims, meaning 16—17
Single period securities markets, contingent claims, risk neutral valuation principle 18
Single period securities markets, contingent claims, unattainable 24
Single period securities markets, contingent claims, valuation 16—21
Single period securities markets, discounted gains process 3
Single period securities markets, discounted price process 2—3
Single period securities markets, discounted value process 3
Single period securities markets, dominant trading strategy 4—10 17
Single period securities markets, gains process 2
Single period securities markets, incomplete markets 24—28
Single period securities markets, interest rate 1
Single period securities markets, law of one price 7—8 10 17
Single period securities markets, linear pricing measure 6—7
Single period securities markets, linear programming duality theory 6—7 27
Single period securities markets, model specifications 1—4
Single period securities markets, price movement 2
Single period securities markets, price process 2
Single period securities markets, replicating portfolio 17
Single period securities markets, risk and return 28—31
Single period securities markets, risk neutral probability measures 10 11—16 21—24 28
Single period securities markets, risk premiums 29
Single period securities markets, separating hyperplane theorem 14
Single period securities markets, state price density 28
Single period securities markets, state price vector 28
Single period securities markets, trading strategy 2
Single period securities markets, value process 2
Spot interest rate 200 210—212 215—217
State price density 28 35
State price vector 28
State space 106
State-price deflator 100
Stationary Markov chain 107 108—111
Stochastic integrals 81
Stochastic process models of security prices 77—79
Stopping time, derivatives 135
Stopping time, options 127
Submartingales, multiperiod securities markets 91
Submartingales, options 131 132
Supermartingales, multiperiod securities markets 91
Supermartingales, options 127 129
Swaps 137 229—234
Swaptions 231—234
Term structure model, bonds and interest rate derivatives 200—208 223
Term structure model, forward interest rates 207
Term structure model, interest rates 205—206
Term structure model, zero coupon bond prices 200 219—222
Terminal wealth, maximum utility from consumption and 173—178
Time-homogeneous Markov chain 107
Trading strategies, contingent claims 114
Trading strategies, dominant 4—10 17
Trading strategies, hedging 129
Trading strategies, infinite horizon models 244
Trading strategies, multiperiod securities markets 80 86
Trading strategies, optimal portfolios with constraints 179
Trading strategies, replicating 114—116 129
Trading strategies, self-financing 82—83
Trading strategies, single period securities markets 2
Transition matrices 107
Transition probabilities 107—108
Unattainable contingent claims 24
Undiscounted risky price process 147
Up-and-in calls 123
Up-and-in puts 123
Up-and-out calls 123
Up-and-out puts 123
Value process, American options 125
Value process, finite horizon models 240
Value process, multiperiod securities markets 81—82
Value process, multiperiod securities markets, returns for 85—87
Value process, optimal 153
Value process, options 125
Value process, single period securities markets 2
Volatilities 212—217
Whole yield approach, bonds and interest rate derivatives 217
Yield curve 205—206
Yield curve, models 217—222
Yield to maturity 205
Zero coupon bonds 200
Zero coupon bonds, prices 201—203 208—213
Zero coupon bonds, prices, term structure 219—222
“Almost surely” 239
|
|
|
| Ðåêëàìà |
|
|
|
|
|
Î ïðîåêòå