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Pliska S.R. Ч Introduction to Mathematical Finance
Pliska S.R. Ч Introduction to Mathematical Finance



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Ќазвание: Introduction to Mathematical Finance

јвтор: Pliska S.R.

јннотаци€:

This book grew out of lecture notes organized for a PhD class which Stanley Pliska taight in Japan. The work continued when he was a Distinguished Visiting Fellow at the London School of Economics in 1992. A preliminary version of the book was tried out in a 1994 PhD class at the University of Illinois in Chicago, which provided useful feedback. In January 1995 he took a close-to-final version to the Program on Financial Mathematics at the Isaac Newton Institute for Mathematical Sciences, University of Cambridge. There, parts of the book were used for a course and copies of the whole book were made available to visting researchers


язык: en

–убрика: Ёкономика и финансы/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1997

 оличество страниц: 262

ƒобавлена в каталог: 15.04.2006

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Admissible consumption-investment plans      41 185
Affine function      71
American options      124Ч133 153
Arbitrage free securities market model      143Ч144
Arbitrage opportunities, bonds and interest rate derivatives      201 218
Arbitrage opportunities, contingent claims      116
Arbitrage opportunities, finite horizon models      238 240Ч241 243
Arbitrage opportunities, forward prices and cash stream valuation      138Ч140
Arbitrage opportunities, futures      140 142Ч143
Arbitrage opportunities, infinite horizon models      245 246 248
Arbitrage opportunities, multipenod securities markets      92 96
Arbitrage opportunities, optimal portfolios      151Ч152
Arbitrage opportunities, single period consumption and investment      34
Arbitrage opportunities, single period securities markets      8Ч10 11Ч13 17 24
Arbitrage pricing      116
Arbitrage pricing theory      17
Asset pricing, fundamental theorem of      see УFundamental theorem of asset pricingФ
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      145Ч146
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      120Ч124
Binomial model, interest rate version      208
Binomial model, multiperiod securities markets      100Ч106
Binomial probability distribution      102
Bond options      227Ч229
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      227Ч229
Bonds and interest rate derivatives, caplets      234Ч235
Bonds and interest rate derivatives, caps      234Ч235
Bonds and interest rate derivatives, captions      235Ч237
Bonds and interest rate derivatives, compound options      236
Bonds and interest rate derivatives, contingent claims      222
Bonds and interest rate derivatives, coupon bonds      227Ч229
Bonds and interest rate derivatives, derivative pricing      224
Bonds and interest rate derivatives, filtration      203Ч204 208
Bonds and interest rate derivatives, floorlets      235
Bonds and interest rate derivatives, floors      235
Bonds and interest rate derivatives, floortions      235Ч237
Bonds and interest rate derivatives, forward interest rates      206
Bonds and interest rate derivatives, forward risk adjusted probability measures      222Ч226
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      208Ч217
Bonds and interest rate derivatives, lattice-type interest rate models      226
Bonds and interest rate derivatives, Markov chain models      208Ч217 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      231Ч234
Bonds and interest rate derivatives, receiver swaps      229
Bonds and interest rate derivatives, receiver swaptions      231Ч234
Bonds and interest rate derivatives, risk neutral probability measures      201 203Ч205 218 224
Bonds and interest rate derivatives, riskless interest rate      200
Bonds and interest rate derivatives, spot interest rate      200 210Ч212 215Ч217
Bonds and interest rate derivatives, swaps and swaptions      229Ч234
Bonds and interest rate derivatives, term structure model      200Ч208 223
Bonds and interest rate derivatives, term structure of forward interest rates      207
Bonds and interest rate derivatives, term structure of interest rates      205Ч206
Bonds and interest rate derivatives, term structure of zero coupon bond prices      200 219Ч222
Bonds and interest rate derivatives, volatilities      212Ч217
Bonds and interest rate derivatives, whole yield approach      217
Bonds and interest rate derivatives, yield curve      205Ч206
Bonds and interest rate derivatives, yield curve, models      217Ч222
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      201Ч203 208Ч213
Call options      117
Capital asset pricing model (CAPM) theory      49Ч50
Caplets      234Ч235
Caps      234Ч235
Captions      235Ч237
Carrying cost      138
Cash stream valuation      136Ч140
Chooser options      117Ч118
Collateral      141
Complete markets, derivatives      133Ч134
Complete markets, single period consumption and investment      33Ч58
Complete markets, single period securities markets      21Ч24
Compound options      236
Conditional expectation and martingales      88Ч91
Consumption and terminal wealth, maximum utility from      173Ч178
Consumption processes      40Ч41 162 168 185
Consumption-investment plans      40Ч41 162Ч163 185
Consumption-investment, dynamic programming      162Ч168
Consumption-investment, martingale methods      168Ч173
Consumption-investment, optimal, with constraints      184Ч188
Consumption-investment, optimal, with constraints, risk neutral computational approach      188Ч193
Consumption-investment, problems      40Ч47
Consumption-investment, risk neutral probability measure      168Ч173 (see also УSingle period consumption and investmentФ)
Contingent claims, derivatives      see УDerivativesФ
Contingent claims, derivatives, options      117Ч120
Contingent claims, derivatives, price formula      222
Contingent claims, derivatives, single period securities markets      see УSingle period securities marketsФ
Coupon bonds      227Ч229
Demand functions      68
Derivative pricing      224
Derivatives, binomial model, European options      120Ч124
Derivatives, binomial model, Markov chains      121
Derivatives, binomial model, martingale measures      121
Derivatives, complete and incomplete markets      133
Derivatives, complete and incomplete markets, complete      133Ч134
Derivatives, complete and incomplete markets, contingent claims      134
Derivatives, complete and incomplete markets, incomplete      134Ч136
Derivatives, complete and incomplete markets, multipenod models      133
Derivatives, complete and incomplete markets, risk neutral УconditionalФ 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      117Ч118
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      117Ч120
Derivatives, contingent claims, put options      117
Derivatives, contingent claims, put-call parity      117
Derivatives, contingent claims, replicating trading strategy      114Ч116
Derivatives, contingent claims, risk neutral valuation principle      113
Derivatives, contingent claims, trading strategy      114
Derivatives, forward prices and cash stream valuation      136Ч138
Derivatives, forward prices and cash stream valuation, arbitrage opportunities      138Ч140
Derivatives, forward prices and cash stream valuation, carrying cost      138
Derivatives, futures, arbitrage free securities market model      143Ч144
Derivatives, futures, arbitrage opportunities      140 142Ч143
Derivatives, futures, bank account process      145Ч146
Derivatives, futures, discounted risky price process      147
Derivatives, futures, forward prices compared      140Ч141
Derivatives, futures, margin or collateral      141
Derivatives, futures, martingales      147
Derivatives, futures, options      146Ч148
Derivatives, futures, risk neutral probability measures      143
Derivatives, futures, self-financing      142
Derivatives, futures, undiscounted risky price process      147
Derivatives, options, American      124Ч133
Derivatives, options, attainable American      129
Derivatives, options, barrier options      123
Derivatives, options, call      117
Derivatives, options, chooser      117Ч118
Derivatives, options, contingent claims      117Ч120
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 120Ч124
Derivatives, options, futures      146Ч148
Derivatives, options, hedging trading strategy      129
Derivatives, options, knockout      122Ч123
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 УZero coupon bondsФ
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      2Ч3
Discounted prices      83Ч84
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      87Ч88
Dominant trading strategy      4Ч10 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      162Ч168
Dynamic programming, optimal portfolios      153Ч156
Dynamic programming, portfolio optimization in incomplete markets      193Ч195
Economic considerations, multiperiod securities markets      92 100
Ellipsoid method, linear program solving      250
Equilibrium models      64Ч70
European options      113 120Ч124 231 234
Fictitious security approach, portfolio optimization in incomplete markets      196Ч199
Fictitious security approach, single period consumption and investment      59Ч64
Filtration, bond and interest rate derivatives      203Ч204 208
Filtration, multiperiod securities markets      77Ч79
Finite horizon models      238Ч243
Floorlets      235
Floors      235
Floortions      235Ч237
Forward interest rates      206
Forward prices      136Ч140 140Ч141
Forward risk adjusted probability measures      222Ч226
Forward spot interest rates      206
Forward start swaps      229
Fundamental theorem of asset pricing, finite horizon models      238 240Ч243
Fundamental theorem of asset pricing, infinite horizon models      246Ч248
Futures      see УDerivativesФ
Gains process, multiperiod securities markets      81Ч82
Gains process, multiperiod securities markets, returns for      85Ч87
Gains process, single period securities markets      2
Hahn Banach theorem      14
Hedging trading strategy      129
Incomplete markets, derivatives      134Ч136
Incomplete markets, portfolio optimization in      193Ч199
Incomplete markets, single period consumption and investment      58Ч64
Incomplete markets, single period securities markets      24Ч28
Infinite horizon models      243Ч249
Infinite sample spaces models, arbitrage opportunities      238 240Ч241 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      238Ч243
Infinite sample spaces models, fundamental theorem of asset pricing      238 240Ч243 246Ч248
Infinite sample spaces models, infinite horizon models      243Ч249
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      73Ч76
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 210Ч212 215Ч217
Interest rates, term structure      205Ч206
Knockout options      122Ч123
Lagrange multiplier approach, portfolio optimization in incomplete markets      195Ч196
Lattice, Markov chain models      208Ч217
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      7Ч8 10 17
Linear pricing measure, multiperiod securities markets      99Ч100
Linear pricing measure, single period securities markets      6Ч7
Linear programming      250Ч253
Linear programming duality theory, single period securities markets      6Ч7 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      208Ч217 226
Markov chains, stationary      107 108Ч111
Markov chains, time-homogeneous      107
Markov chains, transition probabilities      107Ч108
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      168Ч173
Martingale methods, optimal portfolios      156Ч162
Martingales, bonds and interest rate derivatives      201 223 224
Martingales, finite horizon models      241
Martingales, futures      147
Martingales, multiperiod securities markets      88Ч91 94Ч95 98
Maximum utility from consumption and terminal wealth      173 8
Mean-variance portfolio analysis      47Ч51
Model specifications, filtrations, and stochastic processes      see УMultiperiod securities marketsФ
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      100Ч106
Multiperiod securities markets, binomial probability distribution      102
Multiperiod securities markets, conditional expectation and martingales      88Ч91
Multiperiod securities markets, economic considerations      92Ч100
Multiperiod securities markets, interest rates      72
Multiperiod securities markets, law of one price      99
Multiperiod securities markets, linear pricing measures      99Ч100
Multiperiod securities markets, Markov models      106Ч111
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