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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)

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)

- Sara Biagini, Bruno Bouchard, Constantinos Kardaras, Marcel Nutz
- 2015

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)

Portfolio turnpikes state that, as the investment horizon increases, optimal portfolios for generic utilities converge to those of isoelastic utilities. This paper proves three kinds of turnpikes. In a general semimartingale setting, the abstract turnpike states that optimal final payoffs and portfolios converge under their myopic probabilities. In… (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)

We develop a new theory for pricing call type American options in complete markets which do not necessarily admit an equivalent local martingale measure. This resolve an open Let β be a strictly positive and nonincreasing process with β 0 = 1 and S be a strictly positive semimartingale. We assume that there is a strictly positive local martingale Z with Z 0… (More)

In a financial market model, we consider variations of the problem of minimizing the expected time to upcross a certain wealth level. For exponential Lévy markets, we show the asymptotic optimality of the growth-optimal portfolio for the above problem and obtain tight bounds for the value function for any wealth level. In an Itô market, we employ the… (More)

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