The Mathematics of ArbitrageSpringer Science & Business Media, 14 de fev. de 2006 - 371 páginas Proof of the "Fundamental Theorem of Asset Pricing" in its general form by Delbaen and Schachermayer was a milestone in the history of modern mathematical finance and now forms the cornerstone of this book. Puts into book format a series of major results due mostly to the authors of this book. Embeds highest-level research results into a treatment amenable to graduate students, with introductory, explanatory background. Awaited in the quantitative finance community. |
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The Mathematics of Arbitrage, Volume 13 Freddy Delbaen,Walter Schachermayer Prévia não disponível - 2006 |
Termos e frases comuns
1-admissible admissible integrands allows apply arbitrage argument asset assume assumption Banach space called Chap Clearly closed condition cone consider constant contingent claim continuous converges Corollary decomposition defined definition denote economic element equals equivalent example existence fact filtration Finance finite fixed follows free lunch function give given hence implies increasing inequality investment jumps Lemma limit local martingale martingale measure Mathematical maximal measure Q necessarily NFLVR no-arbitrage norm Note numéraire obtain option precisely predictable process present probability measure problem process H proof Proposition prove random variable Rd-valued relation Remark replace respect result risk satisfies Sect sequence simple space stochastic integral stopping strategy strictly positive subsequence suppose surely tends to zero Theorem theory topology trading strategy uniformly integrable variation
Passagens mais conhecidas
Página 9 - This brings us to a first — informal and intuitive — definition of arbitrage: an arbitrage opportunity is the possibility to make a profit in a financial market without risk and without net investment of capital. The principle of no- arbitrage states that a mathematical model of a financial market should not allow for arbitrage possibilities.
Página 9 - A currency option may be defined as a contract between two parties — a buyer and a seller — whereby the buyer of the option has the right but not the obligation, to buy...
Página 372 - Heath, (1972), Existence of equilibria in economics with infinitely many commodities.
Página 9 - Euro/Dollar example above, we consider a still extremely simple mathematical model of a financial market: there are two assets, called the bond and the stock. The bond is riskless, hence by definition we know what it is worth tomorrow. For (mainly notational) simplicity we neglect interest rates and assume that the price of a bond equals 1€ today as well as tomorrow, ie, Bo = Bi...
Página 13 - Variations of the Example Although the preceding "toy example" is extremely simple and, of course, far from reality, it contains the heart of the matter: the possibility of replicating a contingent claim, eg an option, by trading on the existing assets and to apply the no-arbitrage principle.