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E-raamat: Financial Mathematics: Theory and Problems for Multi-period Models

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  • Formaat: PDF+DRM
  • Sari: La Matematica per il 3+2
  • Ilmumisaeg: 05-Apr-2012
  • Kirjastus: Springer Verlag
  • Keel: eng
  • ISBN-13: 9788847025387
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Financial Mathematics: Theory and Problems for Multi-period ModelsSuurem pilt
  • Formaat: PDF+DRM
  • Sari: La Matematica per il 3+2
  • Ilmumisaeg: 05-Apr-2012
  • Kirjastus: Springer Verlag
  • Keel: eng
  • ISBN-13: 9788847025387
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With the Bologna Accords a bachelor-master-doctor curriculum has been introduced in various countries with the intention that students may enter the job market already at the bachelor level. Since financial Institutions provide non negligible job opportunities also for mathematicians, and scientists in general, it appeared to be appropriate to have a financial mathematics course already at the bachelor level in mathematics. Most mathematical techniques in use in financial mathematics are related to continuous time models and require thus notions from stochastic analysis that bachelor students do in general not possess. Basic notions and methodologies in use in financial mathematics can however be transmitted to students also without the technicalities from stochastic analysis by using discrete time (multi-period) models for which general notions from Probability suffice and these are generally familiar to students not only from science courses, but also from economics with quantitative curricula. There do not exists many textbooks for multi-period models and the present volume is intended to fill in this gap. It deals with the basic topics in financial mathematics and, for each topic, there is a theoretical section and a problem section. The latter includes a great variety of possible problems with complete solution.

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From the reviews:

The authors present a textbook for a course in financial mathematics at the bachelor level. It presents a plethora of highly instructive problems/exercises and their solutions, enabling the reader to acquire a confident practical working knowledge of the material. These advantages make the book exceptionally valuable for students; moreover, since the setup of the book is the one used in industry applications of mathematical finance, it can be a very useful read for practitioners interested in the theoretical aspects of the applied methods. (Tamás Mátrai, Zentralblatt MATH, Vol. 1247, 2012)

1 Pricing and hedging
1(60)
1.1 Primary securities and strategies
2(5)
1.1.1 Discrete time markets
2(1)
1.1.2 Self-financing and predictable portfolios
3(2)
1.1.3 Relative portfolio
5(1)
1.1.4 Discounted market
6(1)
1.2 Arbitrage and martingale measures
7(2)
1.3 Pricing and hedging
9(5)
1.3.1 Derivative securities
9(1)
1.3.2 Arbitrage pricing
10(3)
1.3.3 Hedging
13(1)
1.3.4 Put-Call parity
13(1)
1.4 Market models
14(8)
1.4.1 Binomial model
14(4)
1.4.2 Trinomial model
18(4)
1.5 On pricing and hedging in incomplete markets
22(1)
1.6 Change of numeraire
23(5)
1.6.1 A particular case
23(2)
1.6.2 General case
25(3)
1.7 Solved problems
28(33)
2 Portfolio optimization
61(104)
2.1 Maximization of expected utility
62(10)
2.1.1 Strategies with consumption
62(3)
2.1.2 Utility functions
65(2)
2.1.3 Expected utility of terminal wealth
67(3)
2.1.4 Expected utility from intermediate consumption and terminal wealth
70(2)
2.2 "Martingale" method
72(16)
2.2.1 Complete market: terminal wealth
72(6)
2.2.2 Incomplete market: terminal wealth
78(3)
2.2.3 Complete market: intermediate consumption
81(5)
2.2.4 Complete market: intermediate consumption and terminal wealth
86(2)
2.3 Dynamic Programming Method
88(6)
2.3.1 Recursive algorithm
88(4)
2.3.2 Proof of Theorem 2.32
92(2)
2.4 Logarithmic utility: examples
94(24)
2.4.1 Terminal utility in the binomial model: MG method
94(2)
2.4.2 Terminal utility in the binomial model: DP method
96(3)
2.4.3 Terminal utility in the completed trinomial model: MG method
99(2)
2.4.4 Terminal utility in the completed trinomial model: DP method
101(2)
2.4.5 Terminal utility in the standard trinomial model: DP method
103(3)
2.4.6 Intermediate consumption in the binomial model: MG method
106(3)
2.4.7 Intermediate consumption in the binomial model: DP method
109(4)
2.4.8 Intermediate consumption in the completed trinomial model: MG method
113(1)
2.4.9 Optimal consumption in the completed trinomial model: DP method
114(1)
2.4.10 Intermediate consumption in the standard trinomial model: DP method
115(3)
2.5 Solved problems
118(47)
3 American options
165(58)
3.1 American derivatives and early exercise strategies
166(14)
3.1.1 Arbitrage pricing
167(2)
3.1.2 Arbitrage price in a complete market
169(6)
3.1.3 Optimal exercise strategies
175(3)
3.1.4 Hedging strategies
178(2)
3.2 American and European options
180(3)
3.3 Solved problems
183(40)
3.3.1 Preliminaries
183(1)
3.3.2 Solved problems
184(39)
4 Interest rates
223(64)
4.1 Bonds and interest rates
224(3)
4.2 Market models for interest rates
227(3)
4.3 Short models
230(7)
4.3.1 Affine models
232(1)
4.3.2 Discrete time Hull-White model
233(4)
4.4 Forward models
237(7)
4.4.1 Binomial forward model
239(2)
4.4.2 Multinomial forward model
241(3)
4.5 Interest rate derivatives
244(8)
4.5.1 Caps and Floors
244(3)
4.5.2 Interest Rate Swaps
247(3)
4.5.3 Swaptions and Swap Rate
250(2)
4.6 Solved problems
252(35)
4.6.1 Recalling the basic models
252(3)
4.6.2 Options on T-bonds
255(7)
4.6.3 Caps and Floors
262(9)
4.6.4 Swap Rates and Payer Forward Swaps
271(5)
4.6.5 Swaptions
276(11)
References 287
Andrea Pascucci is Professor of Financial Mathematics at the University of Bologna where he is also director of a master in Math Finance. His research interests include partial differential equations and stochastic analysis with applications to finance, with a special focus on option pricing, volatility modeling and analytical methods.

Wolfgang Runggaldier is Professor in Probability at the University of Padova. His research interests are in the general area of stochastic dynamical systems and, since about twenty years, mainly in financial mathematics. In this latter area he has been conducting extensive research, lecturing in various places, supervising students, organizing meetings and workshops and taking part in editorial boards.
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