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We study the existence of the numéraire portfolio under predictable convex constraints in a general semimartingale model of a financial market. The numéraire portfolio generates a wealth process, with respect to which the relative wealth processes of all other portfolios are supermartingales. Necessary and sufficient conditions for the existence of the… (More)

The absence of arbitrages of the first kind, a weakening of the " No Free Lunch with Vanishing Risk " condition of [2], is analyzed in a general semimartingale financial market model. In the spirit of the Fundamental Theorem of Asset Pricing, it is shown that there is equivalence between the absence of arbitrages of the first kind and the existence of a… (More)

- TOMOYUKI ICHIBA, VASSILIOS PAPATHANAKOS, ADRIAN BANNER, IOANNIS KARATZAS, Constantinos Kardaras, Erhan Bayraktar
- 2009

We study Atlas-type models of equity markets with local characteristics that depend on both name and rank, and in ways that induce a stability of the capital distribution. Ergodic properties and rankings of processes are examined with reference to the theory of reflected Brownian motions in polyhedral domains. In the context of such models, we discuss… (More)

An equity 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 Itô-process model initiated by Samuelson (1965) we formulate this property (and the allied, successively weaker notions of " weak diversity " and " asymptotic weak diversity ") in precise… (More)

We provide equivalence of numerous no-free-lunch 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,… (More)

The numéraire portfolio in a financial market is the unique positive wealth process that makes all other nonnegative wealth processes supermartingales, when deflated by it. The numéraire portfolio depends on market characteristics, which include: (a) the information flow available to acting agents, given by a filtration; (b) the statistical evolution of the… (More)

We study a continuous-time financial market with continuous price processes under model uncertainty, modeled via a family P of possible physical measures. A robust notion NA 1 (P) of no-arbitrage of the first kind is introduced; it postulates that a nonnegative, nonvanishing claim cannot be superhedged for free by using simple trading strategies. Our first… (More)

We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of the state space. We allow for various types of model behavior: the volatility process in our model can potentially… (More)

We provide an axiomatic foundation for the representation of numéraire-invariant preferences of agents acting in a financial market. In a static environment, the simple axioms turn out to be equivalent to the following choice rule: the agent prefers one outcome over another if and only if the expected (under the agent's subjective probability) relative rate… (More)

In a general semimartingale financial model, we study the stability of the No Arbitrage of the First Kind (NA1) (or, equivalently, No Unbounded Profit with Bounded Risk) condition under initial and under progressive filtration enlargements. In both cases, we provide a simple and general condition which is sufficient to ensure this stability for any fixed… (More)