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| Àâòîðèçàöèÿ |
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| Ïîèñê ïî óêàçàòåëÿì |
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| Pliska S.R. — Introduction to Mathematical Finance |
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| Ïðåäìåòíûé óêàçàòåëü |
Admissible consumption-investment plans 41 185
Affine function 71
American options 124—133 153
Arbitrage free securities market model 143—144
Arbitrage opportunities, bonds and interest rate derivatives 201 218
Arbitrage opportunities, contingent claims 116
Arbitrage opportunities, finite horizon models 238 240—241 243
Arbitrage opportunities, forward prices and cash stream valuation 138—140
Arbitrage opportunities, futures 140 142—143
Arbitrage opportunities, infinite horizon models 245 246 248
Arbitrage opportunities, multipenod securities markets 92 96
Arbitrage opportunities, optimal portfolios 151—152
Arbitrage opportunities, single period consumption and investment 34
Arbitrage opportunities, single period securities markets 8—10 11—13 17 24
Arbitrage pricing 116
Arbitrage pricing theory 17
Asset pricing, fundamental theorem of see “Fundamental theorem of asset pricing”
Attainable American options 129
Attainable consumption processes 168
Attainable contingent claims 17 113
Attainable wealths 38
Bank account process, contingent claims 117
Bank account process, finite horizon models 239
Bank account process, futures 145—146
Bank account process, multiperiod securities markets 72
Bank account process, single period securities markets 1
Barrier options 123
Bernoulli processes 101
Binomial coefficients 102
Binomial model, European options 120—124
Binomial model, interest rate version 208
Binomial model, multiperiod securities markets 100—106
Binomial probability distribution 102
Bond options 227—229
Bonds and interest rate derivatives, arbitrage opportunities 201 218
Bonds and interest rate derivatives, binomial model, interest rate version 208
Bonds and interest rate derivatives, bond options 227—229
Bonds and interest rate derivatives, caplets 234—235
Bonds and interest rate derivatives, caps 234—235
Bonds and interest rate derivatives, captions 235—237
Bonds and interest rate derivatives, compound options 236
Bonds and interest rate derivatives, contingent claims 222
Bonds and interest rate derivatives, coupon bonds 227—229
Bonds and interest rate derivatives, derivative pricing 224
Bonds and interest rate derivatives, filtration 203—204 208
Bonds and interest rate derivatives, floorlets 235
Bonds and interest rate derivatives, floors 235
Bonds and interest rate derivatives, floortions 235—237
Bonds and interest rate derivatives, forward interest rates 206
Bonds and interest rate derivatives, forward risk adjusted probability measures 222—226
Bonds and interest rate derivatives, forward spot interest rates 206
Bonds and interest rate derivatives, forward start swaps 229
Bonds and interest rate derivatives, lattice, Markov chain models 208—217
Bonds and interest rate derivatives, lattice-type interest rate models 226
Bonds and interest rate derivatives, Markov chain models 208—217 226
Bonds and interest rate derivatives, martingales 201 223 224
Bonds and interest rate derivatives, payer swaps 229
Bonds and interest rate derivatives, payer swaptions 231—234
Bonds and interest rate derivatives, receiver swaps 229
Bonds and interest rate derivatives, receiver swaptions 231—234
Bonds and interest rate derivatives, risk neutral probability measures 201 203—205 218 224
Bonds and interest rate derivatives, riskless interest rate 200
Bonds and interest rate derivatives, spot interest rate 200 210—212 215—217
Bonds and interest rate derivatives, swaps and swaptions 229—234
Bonds and interest rate derivatives, term structure model 200—208 223
Bonds and interest rate derivatives, term structure of forward interest rates 207
Bonds and interest rate derivatives, term structure of interest rates 205—206
Bonds and interest rate derivatives, term structure of zero coupon bond prices 200 219—222
Bonds and interest rate derivatives, volatilities 212—217
Bonds and interest rate derivatives, whole yield approach 217
Bonds and interest rate derivatives, yield curve 205—206
Bonds and interest rate derivatives, yield curve, models 217—222
Bonds and interest rate derivatives, yield to maturity 205
Bonds and interest rate derivatives, zero coupon bonds 200
Bonds and interest rate derivatives, zero coupon bonds, prices 201—203 208—213
Call options 117
Capital asset pricing model (CAPM) theory 49—50
Caplets 234—235
Caps 234—235
Captions 235—237
Carrying cost 138
Cash stream valuation 136—140
Chooser options 117—118
Collateral 141
Complete markets, derivatives 133—134
Complete markets, single period consumption and investment 33—58
Complete markets, single period securities markets 21—24
Compound options 236
Conditional expectation and martingales 88—91
Consumption and terminal wealth, maximum utility from 173—178
Consumption processes 40—41 162 168 185
Consumption-investment plans 40—41 162—163 185
Consumption-investment, dynamic programming 162—168
Consumption-investment, martingale methods 168—173
Consumption-investment, optimal, with constraints 184—188
Consumption-investment, optimal, with constraints, risk neutral computational approach 188—193
Consumption-investment, problems 40—47
Consumption-investment, risk neutral probability measure 168—173 (see also “Single period consumption and investment”)
Contingent claims, derivatives see “Derivatives”
Contingent claims, derivatives, options 117—120
Contingent claims, derivatives, price formula 222
Contingent claims, derivatives, single period securities markets see “Single period securities markets”
Coupon bonds 227—229
Demand functions 68
Derivative pricing 224
Derivatives, binomial model, European options 120—124
Derivatives, binomial model, Markov chains 121
Derivatives, binomial model, martingale measures 121
Derivatives, complete and incomplete markets 133
Derivatives, complete and incomplete markets, complete 133—134
Derivatives, complete and incomplete markets, contingent claims 134
Derivatives, complete and incomplete markets, incomplete 134—136
Derivatives, complete and incomplete markets, multipenod models 133
Derivatives, complete and incomplete markets, risk neutral “conditional” probability measures 134
Derivatives, complete and incomplete markets, stopping time 135
Derivatives, contingent claims, arbitrage opportunity 116
Derivatives, contingent claims, arbitrage pricing 116
Derivatives, contingent claims, attainable 113
Derivatives, contingent claims, bank account process 117
Derivatives, contingent claims, call options 117
Derivatives, contingent claims, chooser options 117—118
Derivatives, contingent claims, definition 112
Derivatives, contingent claims, law of one price 114
Derivatives, contingent claims, look-back options 120
Derivatives, contingent claims, marketable 113
Derivatives, contingent claims, martingale measures 118
Derivatives, contingent claims, options 117—120
Derivatives, contingent claims, put options 117
Derivatives, contingent claims, put-call parity 117
Derivatives, contingent claims, replicating trading strategy 114—116
Derivatives, contingent claims, risk neutral valuation principle 113
Derivatives, contingent claims, trading strategy 114
Derivatives, forward prices and cash stream valuation 136—138
Derivatives, forward prices and cash stream valuation, arbitrage opportunities 138—140
Derivatives, forward prices and cash stream valuation, carrying cost 138
Derivatives, futures, arbitrage free securities market model 143—144
Derivatives, futures, arbitrage opportunities 140 142—143
Derivatives, futures, bank account process 145—146
Derivatives, futures, discounted risky price process 147
Derivatives, futures, forward prices compared 140—141
Derivatives, futures, margin or collateral 141
Derivatives, futures, martingales 147
Derivatives, futures, options 146—148
Derivatives, futures, risk neutral probability measures 143
Derivatives, futures, self-financing 142
Derivatives, futures, undiscounted risky price process 147
Derivatives, options, American 124—133
Derivatives, options, attainable American 129
Derivatives, options, barrier options 123
Derivatives, options, call 117
| Derivatives, options, chooser 117—118
Derivatives, options, contingent claims 117—120
Derivatives, options, down-and-in calls 123
Derivatives, options, down-and-in puts 123
Derivatives, options, down-and-out calls 123
Derivatives, options, down-and-out puts 123
Derivatives, options, European 113 120—124
Derivatives, options, futures 146—148
Derivatives, options, hedging trading strategy 129
Derivatives, options, knockout 122—123
Derivatives, options, look-back 120
Derivatives, options, marketable American 129
Derivatives, options, optional sampling theorem 131
Derivatives, options, put 117
Derivatives, options, replicating trading strategy 129
Derivatives, options, stopping time 127
Derivatives, options, submartingales 131 132
Derivatives, options, supermartingales 127 129
Derivatives, options, up-and-in calls 123
Derivatives, options, up-and-in puts 123
Derivatives, options, up-and-out calls 123
Derivatives, options, up-and-outputs 123
Derivatives, options, value process 125
Derivatives, swaps 137
Discount bonds see “Zero coupon bonds”
Discounted gains process, finite horizon models 240
Discounted gains process, multiperiod securities markets 83
Discounted gains process, single period securities markets 3
Discounted price process, finite horizon models 240
Discounted price process, Markov models 108
Discounted price process, multiperiod securities markets 83
Discounted price process, returns for multiperiod securities markets 85
Discounted price process, single period securities markets 2—3
Discounted prices 83—84
Discounted risky price process 147
Discounted value process, finite horizon models 240
Discounted value process, multiperiod securities markets 83
Discounted value process, single period securities markets 3
Dividend processes 87—88
Dominant trading strategy 4—10 17
Down-and-in calls 123
Down-and-in puts 123
Down-and-out calls 123
Down-and-out puts 123
Dynamic programming, consumption-investment 162—168
Dynamic programming, optimal portfolios 153—156
Dynamic programming, portfolio optimization in incomplete markets 193—195
Economic considerations, multiperiod securities markets 92 100
Ellipsoid method, linear program solving 250
Equilibrium models 64—70
European options 113 120—124 231 234
Fictitious security approach, portfolio optimization in incomplete markets 196—199
Fictitious security approach, single period consumption and investment 59—64
Filtration, bond and interest rate derivatives 203—204 208
Filtration, multiperiod securities markets 77—79
Finite horizon models 238—243
Floorlets 235
Floors 235
Floortions 235—237
Forward interest rates 206
Forward prices 136—140 140—141
Forward risk adjusted probability measures 222—226
Forward spot interest rates 206
Forward start swaps 229
Fundamental theorem of asset pricing, finite horizon models 238 240—243
Fundamental theorem of asset pricing, infinite horizon models 246—248
Futures see “Derivatives”
Gains process, multiperiod securities markets 81—82
Gains process, multiperiod securities markets, returns for 85—87
Gains process, single period securities markets 2
Hahn Banach theorem 14
Hedging trading strategy 129
Incomplete markets, derivatives 134—136
Incomplete markets, portfolio optimization in 193—199
Incomplete markets, single period consumption and investment 58—64
Incomplete markets, single period securities markets 24—28
Infinite horizon models 243—249
Infinite sample spaces models, arbitrage opportunities 238 240—241 243 245 246 248
Infinite sample spaces models, bank account process 239
Infinite sample spaces models, discounted gains process 240
Infinite sample spaces models, discounted price process 240
Infinite sample spaces models, discounted value process 240
Infinite sample spaces models, finite horizon models 238—243
Infinite sample spaces models, fundamental theorem of asset pricing 238 240—243 246—248
Infinite sample spaces models, infinite horizon models 243—249
Infinite sample spaces models, linear programming 238
Infinite sample spaces models, martingales 241
Infinite sample spaces models, risk neutral probability measure 238 241 243 246
Infinite sample spaces models, separating hyperplane theorem 238
Infinite sample spaces models, trading strategies 244
Infinite sample spaces models, value process 240
Information structures 73—76
Interest rates, binomial model 208
Interest rates, forward 206
Interest rates, forward, term structure 207
Interest rates, lattice-type models 226
Interest rates, multiperiod securities markets 72
Interest rates, riskless 200
Interest rates, single period securities markets 1
Interest rates, spot 200 210—212 215—217
Interest rates, term structure 205—206
Knockout options 122—123
Lagrange multiplier approach, portfolio optimization in incomplete markets 195—196
Lattice, Markov chain models 208—217
Lattice-type interest rate models 226
Law of one price, contingent claims 114
Law of one price, multiperiod securities markets 99
Law of one price, single period securities markets 7—8 10 17
Linear pricing measure, multiperiod securities markets 99—100
Linear pricing measure, single period securities markets 6—7
Linear programming 250—253
Linear programming duality theory, single period securities markets 6—7 27
Linear programming, finite horizon models 238
Look-back options 120
Margin, futures 141
Marginal utility of terminal wealth 35
Marketable American options 129
Marketable contingent claims 17 113
Markov chains 121
Markov chains, discounted price process 108
Markov chains, models 208—217 226
Markov chains, stationary 107 108—111
Markov chains, time-homogeneous 107
Markov chains, transition probabilities 107—108
Markov models, multiperiod securities markets 106 11
Martingale measures, contingent claims 118
Martingale measures, European options 121
Martingale measures, multiperiod securities markets 93 97
Martingale methods, consumption-investment 168—173
Martingale methods, optimal portfolios 156—162
Martingales, bonds and interest rate derivatives 201 223 224
Martingales, finite horizon models 241
Martingales, futures 147
Martingales, multiperiod securities markets 88—91 94—95 98
Maximum utility from consumption and terminal wealth 173 8
Mean-variance portfolio analysis 47—51
Model specifications, filtrations, and stochastic processes see “Multiperiod securities markets”
Multiperiod models, derivatives 133
Multiperiod securities markets, arbitrage opportunities 92 96
Multiperiod securities markets, bank account processes 72
Multiperiod securities markets, Bernoulli processes 101
Multiperiod securities markets, binomial coefficients 102
Multiperiod securities markets, binomial model 100—106
Multiperiod securities markets, binomial probability distribution 102
Multiperiod securities markets, conditional expectation and martingales 88—91
Multiperiod securities markets, economic considerations 92—100
Multiperiod securities markets, interest rates 72
Multiperiod securities markets, law of one price 99
Multiperiod securities markets, linear pricing measures 99—100
Multiperiod securities markets, Markov models 106—111
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