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23
The NoArbitrage Property under a change of numéraire
 Stochastics and Stochastic Reports
, 1995
"... Abstract. For a price process that has an equivalent risk neutral measure, we investigate if the same property holds when the numeraire is changed. We give necessary and su cient conditions under which the price process of a particular asset which should be thought of as a di erent currency can be ..."
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Cited by 29 (11 self)
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Abstract. For a price process that has an equivalent risk neutral measure, we investigate if the same property holds when the numeraire is changed. We give necessary and su cient conditions under which the price process of a particular asset which should be thought of as a di erent currency can be chosen as new numeraire. The result is related to the characterization of attainable claims that can be hedged. Roughly speaking: the asset representing the new currency is a reasonable investment (in terms of the old currency) if and only if the market does not permit arbitrage opportunities in terms of the new currency as numeraire. This rough but economically meaningful idea is given a precise content in this paper. The main ingredients are a duality relation as well as a result on maximal elements. The paper also generalizes results previously obtained by Jacka, AnselStricker and the authors.
The importance of strictly local martingales; applications to radial OrnsteinUhlenbeck processes
, 1998
"... this paper we encounter a number of examples of strictly local martingales, ..."
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Cited by 12 (1 self)
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this paper we encounter a number of examples of strictly local martingales,
Strict local martingales, bubbles, and no early exercise
, 2007
"... We show pathological behavior of asset price processes modeled by continuous strict local martingales under a riskneutral measure. The inspiration comes from recent results on financial bubbles. We analyze, in particular, the effect of the strict nature of the local martingale on the usual formula ..."
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Cited by 5 (0 self)
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We show pathological behavior of asset price processes modeled by continuous strict local martingales under a riskneutral measure. The inspiration comes from recent results on financial bubbles. We analyze, in particular, the effect of the strict nature of the local martingale on the usual formula for the price of a European call option, especially a strong anomaly when call prices decay monotonically with maturity. A complete and detailed analysis for the archetypical strict local martingale, the reciprocal of a three dimensional Bessel process, has been provided. Our main tool is based on a general htransform technique (due to Delbaen and Schachermayer) to generate positive strict local martingales. This gives the basis for a statistical test to verify a suspected bubble is indeed one (or not).
Diversity and relative arbitrage in equity markets
 Finance Stoch
, 2005
"... A financial market is called “diverse ” if no single stock is ever allowed to dominate the entire market in terms of relative capitalization. In the context of the standard Itôprocess model initiated by Samuelson (1965) we formulate this property (and the allied, successively weaker notions of “wea ..."
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Cited by 5 (2 self)
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A financial market is called “diverse ” if no single stock is ever allowed to dominate the entire market in terms of relative capitalization. In the context of the standard Itôprocess model initiated by Samuelson (1965) we formulate this property (and the allied, successively weaker notions of “weak diversity ” and “asymptotic weak diversity”) in precise terms. We show that diversity is possible to achieve, but delicate. Several illustrative examples are provided, which demonstrate that weaklydiverse financial markets contain relative arbitrage opportunities: it is possible to outperform (or underperform) such markets over arbitrary timehorizons. The existence of such relative arbitrage does not interfere with the development of option pricing, and has interesting consequences for the pricing of longterm warrants and for putcall parity. Several open questions are suggested for further study.
No Arbitrage Without Semimartingales, The annals of applied probability
"... We show that with suitable restrictions on allowable trading strategies, one has no arbitrage in settings where the traditional theory would admit arbitrage possibilities. In particular, price processes that are not semimartingales are possible in our setting, for example fractional Brownian motion. ..."
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Cited by 5 (1 self)
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We show that with suitable restrictions on allowable trading strategies, one has no arbitrage in settings where the traditional theory would admit arbitrage possibilities. In particular, price processes that are not semimartingales are possible in our setting, for example fractional Brownian motion. 1
Free Lunch and Arbitrage Possibilities in a Financial Market Model With an Insider
, 1999
"... We consider financial market models based on Wiener space with two agents on di#erent information levels: a regular agent whose information is contained in the natural filtration of the Wiener process W , and an insider who possesses some extra information from the beginning of the trading interval, ..."
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Cited by 4 (2 self)
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We consider financial market models based on Wiener space with two agents on di#erent information levels: a regular agent whose information is contained in the natural filtration of the Wiener process W , and an insider who possesses some extra information from the beginning of the trading interval, given by a random variable L which contains information from the whole time interval. Our main concern are variables L describing the maximum of a pricing rule. Since for such L the conditional laws given the smaller knowledge of the regular trader up to fixed times are not absolutely continuous with respect to the law of L, this class of examples cannot be treated by means of the enlargement of filtration techniques as applied so far. We therefore use elements of a Malliavin and Ito calculus for measure valued random variables to give criteria for the preservation of the semimartingale property, the absolute continuity of the conditional laws of L with respect to its law, and the absence o...
EQUITY MARKETS
, 2003
"... A financial market is called “diverse ” if no single stock is ever allowed to dominate the entire market in terms of relative capitalization. In the context of the standard Itôprocess model initiated by Samuelson (1965) we formulate this property (and the allied, successively weaker notions of “wea ..."
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Cited by 3 (0 self)
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A financial market is called “diverse ” if no single stock is ever allowed to dominate the entire market in terms of relative capitalization. In the context of the standard Itôprocess model initiated by Samuelson (1965) we formulate this property (and the allied, successively weaker notions of “weak diversity ” and “asymptotic weak diversity”) in precise terms. We show that diversity is possible to achieve, but delicate. Several illustrative examples are provided, which demonstrate that weaklydiverse financial markets contain relative arbitrage opportunities: it is possible to outperform (or underperform) such markets over arbitrary timehorizons. The existence of such relative arbitrage does not interfere with the development of option pricing, and has interesting consequences for the pricing of longterm warrants and for putcall parity. Several open questions are suggested for further study.
NoFreeLunch equivalences for exponential Lévy models under convex constraints on investment
, 2006
"... Abstract. We provide equivalence of numerous nofreelunch type conditions for financial markets where the asset prices are modeled as exponential Lévy processes, under possible convex constraints in the use of investment strategies. The general message is the following: if any kind of free lunch ex ..."
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Cited by 3 (2 self)
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Abstract. We provide equivalence of numerous nofreelunch type conditions for financial markets where the asset prices are modeled as exponential Lévy processes, under possible convex constraints in the use of investment strategies. The general message is the following: if any kind of free lunch exists in these models it has to be of the most egregious type, generating an increasing wealth. Furthermore, we connect the previous to the existence of the numéraire portfolio, both for its particular expositional clarity in exponential Lévy models and as a first step in obtaining analogues of the nofreelunch equivalences in general semimartingale models, a task that is taken on in Karatzas and Kardaras [21]. 0.1. Discussion. An exponential Lévy process — as its name suggests — is simply the exponential of a Lévy process. Models of financial markets that assume an exponential Lévy structure for the movement of the stockprice processes have become increasingly popular in the last years, partly because of their analytical tractability (since their distributional
Hedging under arbitrage
, 2010
"... It is shown that delta hedging provides the optimal trading strategy in terms of minimal required initial capital to replicate a given terminal payoff in a continuoustime Markovian context. This holds true in market models where no equivalent local martingale measure exists but only a squareintegr ..."
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Cited by 2 (1 self)
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It is shown that delta hedging provides the optimal trading strategy in terms of minimal required initial capital to replicate a given terminal payoff in a continuoustime Markovian context. This holds true in market models where no equivalent local martingale measure exists but only a squareintegrable market price of risk. A new probability measure is constructed, which takes the place of an equivalent local martingale measure. In order to ensure the existence of the delta hedge, sufficient conditions are derived for the necessary differentiability of expectations indexed over the initial market configuration. The recently often discussed phenomenon of “bubbles” is a special case of the setting in this paper. Several examples at the end illustrate the techniques described in this work.