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- Ioannis Karatzas, Constantinos Kardaras
- Finance and Stochastics
- 2007

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)

- Robert Fernholz, Ioannis Karatzas, Constantinos Kardaras
- Finance and Stochastics
- 2005

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)

- Constantinos Kardaras
- Finance and Stochastics
- 2012

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)

This work aims at a deeper understanding of the mathematical implications of the economically-sound condition of absence of arbitrages of the first kind in a financial market. In the spirit of the Fundamental Theorem of Asset Pricing (FTAP), it is shown here that the absence of arbitrages of the first kind in the market is equivalent to the existence of a… (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 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)

- 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)

- Erhan Bayraktar, Constantinos Kardaras, Hao Xing
- SIAM J. Financial Math.
- 2012

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 perform a stability analysis for the utility maximization problem in a general semimartingale model where both liquid and illiquid assets (random endowments) are present. Small misspecifications of preferences (as modeled via expected utility), as well as views of the world or the market model (as modeled via subjective probabilities) are considered.… (More)

This paper addresses the question of how to invest in an extremely robust growthoptimal way in a market where the instantaneous expected return of the underlying process is unknown. The optimal investment strategy is identified using a generalized version of the principle eigenfunction for an elliptic second-order differential operator which depends on the… (More)