1,721,029 research outputs found
No arbitrage and preferences
No full textWe show that the classical concepts of No Arbitrage (NA) and of No Free Lunch with Vanishing Risk (NFLVR) are intimately linked with the preferences of the agents acting in the market. We point out that the difference, from an economic perspective, between NA and NFLVR rests on selection of the class of monotone, respectively monotone and concave, utility functions that determines the absence of a Market Free Lunch (MFL), a concept introduced in Frittelli 2004. We finally prove the equivalence between the absence of MLF and the existence of an equivalent sigma -martingale measure
Introduction to a theory of value coherent with the no arbitrage principle
No full textThis paper defines the Value of a general claim based on agent's preferences and coherent with the No Arbitrage Principle. This Value is a non trivial extension of the certainty equivalent since it takes into consideration the possibility of partially hedging the risk carried by the claim.
When the market is complete this Value is the unique no arbitrage price. When the risk may not even be partially covered, this Value is the certainty equivalent.
Between these two cases just some of the risk may be hedged and the no arbitrage principle requires the price to lie in the "arbitrage interval". The Value we propose is exactly designed to satisfy this condition
Almost sure characterization of martingales
No full textLet I⊆R+∪{0} be an arbitrary set with 0∈I; Ξ≡(Ω,F,(F_{t})_{t∈I},P) be a complete filtered probability space such that F0 is trivial and complete; χ be a countable family of real adapted stochastic processes on Ξ.
We provide a necessary and sufficient condition for the existence of a probability measure Q, equivalent to the original measure P, under which every process X∈χ is a martingale. Furthermore, this condition is invariant under substitution of P with an equivalent probability measure; hence the theorem characterizes those real adapted stochastic processes on Ξ which can become martingales under some equivalent probability measure.
The theorem we present allows us also to give a satisfactory solution to the so called Fundamental Problem of Asset Pricing which arises in Mathematical Finance; we further provide the financial interpretation of the "no-free-lunch" condition which is equivalent to the existence of a "risk-neutral measure"
On the existence of minimax martingale measures
No full textEmbedding asset pricing in a utility maximization framework leads naturally to the concept of minimax martingale measures. We consider a market model where the price process is assumed to be a R^{d}- semimartingale X and the set of trading strategies consists of all predictable, X- integrable, R^{d} valued processes H for which the stochastic integral (H.X) is uniformly bounded from below. When the market is free of arbitrage, we show that a sufficient condition for the existence of the minimax measure is that the utility function u:R→R is concave and nondecreasing. We also show the equivalence between the No Free Lunch with Vanishing Risk condition, the existence of a separating measure, and a properly defined notion of viability
Dominated families of martingale, supermartingale and quasimartingale laws
No full textAbstractConsider a dominated family L of probability measures; we investigate the question of whether a single probability Q̂ ϵ L equivalent to the whole family L exists. We show that for supermartingale, quasimartingale and martingale laws the answer is positive. We then provide a necessary and sufficient condition for the existence of an equivalent (super, quasi) martingale measure and deduce an alternative characterization of semimartingales. We further study this problem in the context of security markets models and generalize the well-known fundamental theorem of asset pricing to cover the case of markets with frictions
SOME REMARKS ON ARBITRAGE AND PREFERENCES IN SECURITIES MARKET MODELS
No full textWe introduce the notion of a Market Free Lunch that depends on the preferences of all agents participating in the market. In semimartingale models of securities markets, we characterize No Arbitrage (NA) and No Free Lunch with Vanishing Risk (NFLVR) in terms of the Market Free Lunch and show that the difference between NA and NFLVR consists in the selection of the class of monotone, resp. monotone and continuous, utility functions that determines the absence of the Market Free Lunch.
We also provide a direct proof of the equivalence between the absence of a Market Free Lunch, with respect to monotone concave preferences, and the existence of an equivalent (local/sigma) martingale measure
Conditionally evenly convex sets and evenly quasi-convex maps
Full text linkEvenly convex sets in a topological vector space are defined as the intersection of a family of open half spaces. We introduce a generalization of this concept in the conditional framework and provide a generalized version of the bipolar theorem. This notion is then applied to obtain the dual representation of conditionally evenly quasi-convex maps, which turns out to be a fundamental ingredient in the study of quasi-convex dynamic risk measures
Complete duality for quasiconvex dynamic risk measures on modules of the Lp-type
Full text linkIn the conditional setting we provide a complete duality between quasiconvex riskmeasures defined on L0 modules of the Lp type and the appropriate class of dual functions. This is based on a general result which extends the usual Penot-Volle representation for quasiconvex real valued maps
The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets
No full textLet χ be a family of stochastic processes on a given filtered probability space (Ω, "F", ("F" "t" )"t" is an element of "T" , "P") with "T"⊆R + . Under the assumption that the set "M" "e" of equivalent martingale measures for χ is not empty, we give sufficient conditions for the existence of a unique equivalent martingale measure that minimizes the relative entropy, with respect to "P", in the class of martingale measures. We then provide the characterization of the density of the minimal entropy martingale measure, which suggests the equivalence between the maximization of expected exponential utility and the minimization of the relative entropy. Copyright Blackwell Publishers, Inc. 2000.
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