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Financial Mathematics : Theory and Problems for Multi-period Models / by Andrea Pascucci, Wolfgang J. Runggaldier
Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Unitext | SpringerLink BücherPublisher: Milan [u.a.] : Springer, 2012Description: Online-Ressource (IX, 294 p, digital)ISBN:- 9788847025387
- 9788847025370
- 500 650.0285554
- 519
- HB135-147
Contents:
Summary: Pricing and hedging -- Portfolio optimization -- American options -- Interest rates.Summary: 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.PPN: PPN: 1651472599Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
""Title Page ""; ""Copyright Page ""; ""Preface""; ""Table of Contents ""; ""1 Pricing and hedging""; ""1.1 Primary securities and strategies""; ""1.1.1 Discrete time markets""; ""1.1.2 Self-financing and predictable portfolios""; ""1.1.3 Relative portfolio""; ""1.1.4 Discounted market""; ""1.2 Arbitrage and martingale measures""; ""1.3 Pricing and hedging""; ""1.3.1 Derivative securities""; ""1.3.2 Arbitrage pricing""; ""1.3.3 Hedging""; ""1.3.4 Put-Call parity""; ""1.4 Market models""; ""1.4.1 Binomial model""; ""1.4.2 Trinomial model""; ""1.5 On pricing and hedging in incomplete markets""
""1.6 Change of numeraire""""1.6.1 A particular case""; ""1.6.2 General case""; ""1.7 Solved problems""; ""2 Portfolio optimization""; ""2.1 Maximization of expected utility""; ""2.1.1 Strategies with consumption""; ""2.1.2 Utility functions""; ""2.1.3 Expected utility of terminal wealth""; ""2.1.4 Expected utility from intermediate consumption and terminal wealth""; ""2.2 “Martingale� method""; ""2.2.1 Complete market: terminal wealth ""; ""2.2.2 Incomplete market: terminal wealth""; ""2.2.3 Complete market: intermediate consumption""
""2.2.4 Complete market: intermediate consumption and terminal wealth""""2.3 Dynamic Programming Method""; ""2.3.1 Recursive algorithm""; ""2.3.2 Proof of Theorem 2.32""; ""2.4 Logarithmic utility: examples""; ""2.4.1 Terminal utility in the binomial model: MG method""; ""2.4.2 Terminal utility in the binomial model: DP method""; ""2.4.3 Terminal utility in the completed trinomial model: MG method""; ""2.4.4 Terminal utility in the completed trinomial model: DP method""; ""2.4.5 Terminal utility in the standard trinomial model: DP method""
""2.4.6 Intermediate consumption in the binomial model: MG method""""2.4.7 Intermediate consumption in the binomial model: DP method""; ""2.4.8 Intermediate consumption in the completed trinomial model: MG method""; ""2.4.9 Optimal consumption in the completed trinomial model: DP method""; ""2.4.10 Intermediate consumption in the standard trinomial model: DP method""; ""2.5 Solved problems""; ""3 American options""; ""3.1 American derivatives and early exercise strategies""; ""3.1.1 Arbitrage pricing""; ""3.1.2 Arbitrage price in a complete market""; ""3.1.3 Optimal exercise strategies""
""3.1.4 Hedging strategies""""3.2 American and European options""; ""3.3 Solved problems""; ""3.3.1 Preliminaries""; ""3.3.2 Solved problems""; ""4 Interest rates""; ""4.1 Bonds and interest rates""; ""4.2 Market models for interest rates""; ""4.3 Short models""; ""4.3.1 Affine models""; ""4.3.2 Discrete time Hull-White model ""; ""4.4 Forward models""; ""4.4.1 Binomial forward model""; ""4.4.2 Multinomial forward model""; ""4.5 Interest rate derivatives""; ""4.5.1 Caps and Floors""; ""4.5.2 Interest Rate Swaps""; ""4.5.3 Swaptions and Swap Rate""; ""4.6 Solved problems""
""4.6.1 Recalling the basic models""
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