The Mathematics of Arbitrage

130 8 Arbitrage Theory in Continuous Time: an Overview doubles his bet until the first time he wins. If he starts with 1e, his f ...

8.2 The Crucial Lemma 131 Regarding condition (ii) in the above definition: this is a strong and eco- nomically convincing requi ...

132 8 Arbitrage Theory in Continuous Time: an Overview (i) (EMM), i.e., there is a probability measureQ, equivalent toP, such th ...

8.2 The Crucial Lemma 133 up, which will cause the huddle — including your originale— to disappear. Translating this story into ...

134 8 Arbitrage Theory in Continuous Time: an Overview from a good old friend from functional analysis, the theorem of Krein-Smu ...

8.2 The Crucial Lemma 135 Let us compare Lemma 8.2.3 with the previous literature. An important theorem of J. M ́emin [M 80] sta ...

136 8 Arbitrage Theory in Continuous Time: an Overview Using substantially more refined arguments, M. Yor [Y 78a] was able to ex ...

8.2 The Crucial Lemma 137 This result is a good illustration for our philosophy: supposewe know already that the assumption of 8 ...

138 8 Arbitrage Theory in Continuous Time: an Overview One easily verifies (arguing either “mathematically” or “economically”) t ...

8.2 The Crucial Lemma 139 Speaking mathematically, this means that — even whenSis a martingale, as is the case in the example of ...

140 8 Arbitrage Theory in Continuous Time: an Overview Define the stopping timesτkas τk=inf{t|(Hnk·S)t−(Hmk·S)t≥α}, so that we h ...

8.3 Sigma-martingales and the Non-locally Bounded Case 141 Before starting to answer this question, we remark that this question ...

142 8 Arbitrage Theory in Continuous Time: an Overview taking its values in]0,∞[, such that theRd-valued stochastic integralφ·Si ...

8.3 Sigma-martingales and the Non-locally Bounded Case 143 The subtle issue is the implication (ii) ⇒(i) of Theorem 8.3.1. The f ...

144 8 Arbitrage Theory in Continuous Time: an Overview Meσ={Q|Sis aQsigma-martingale}, is dense inMeswith respect to the norm of ...

8.3 Sigma-martingales and the Non-locally Bounded Case 145 as in this example (supposing for the moment thatSis real-valued and ...

146 8 Arbitrage Theory in Continuous Time: an Overview namely zero. This program is worked out in Chap. 14 below in full detail ...

Part II The Original Papers ...

9 A General Version of the Fundamental Theorem of Asset Pricing (1994) 9.1 Introduction ........................................ ...

150 9 Fundamental Theorem of Asset Pricing As an example that this technique has in fact a long history, we quote the use of mor ...