Showing papers by "Ioannis Karatzas published in 2015"
TL;DR: In this article, a negative-parameter variant of the diversity-weighted portfolio studied by Fernholz, Karatzas, and Kardaras (Finance Stoch 9(1):1-27, 2005), which invests in each company a fraction of wealth inversely proportional to the company's market weight (the ratio of its capitalization to that of the entire market), is analyzed.
Abstract: We analyze a negative-parameter variant of the diversity-weighted portfolio studied by Fernholz, Karatzas, and Kardaras (Finance Stoch 9(1):1-27, 2005), which invests in each company a fraction of wealth inversely proportional to the company's market weight (the ratio of its capitalization to that of the entire market). We show that this strategy outperforms the market with probability one, under a non-degeneracy assumption on the volatility structure and the assumption that the market weights admit a positive lower bound. Several modifications of this portfolio, which outperform the market under milder versions of this "no-failure" condition, are put forward, one of which is rank-based. An empirical study suggests that such strategies as studied here have indeed the potential to outperform the market and to be preferable investment opportunities, even under realistic proportional transaction costs.
20 citations
TL;DR: In this article, a negative-parameter variant of the diversity-weighted portfolio studied by Fernholz et al. is analyzed, and it is shown that this strategy outperforms the market with probability one over sufficiently long time-horizons, under a non-degeneracy assumption on the volatility structure and under the assumption that the market weights admit a positive lower bound.
Abstract: We analyze a negative-parameter variant of the diversity-weighted portfolio studied by Fernholz et al. (Finance Stoch 9(1):1–27, 2005), which invests in each company a fraction of wealth inversely proportional to the company’s market weight (the ratio of its capitalization to that of the entire market). We show that this strategy outperforms the market with probability one over sufficiently long time-horizons, under a non-degeneracy assumption on the volatility structure and under the assumption that the market weights admit a positive lower bound. Several modifications of this portfolio are put forward, which outperform the market under milder versions of the latter no-failure condition, and one of which is rank-based. An empirical study suggests that such strategies as studied here have indeed the potential to outperform the market and to be preferable investment opportunities, even under realistic proportional transaction costs.
16 citations
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TL;DR: In this article, the authors construct planar semimartingales that include the Walsh Brownian motion as a special case, and derive Harrison-Shepp-type equations and a change-of-variable formula in the spirit of Freidlin-Sheu for these so-called "Walsh Semi-Martingales".
Abstract: We construct planar semimartingales that include the Walsh Brownian motion as a special case, and derive Harrison-Shepp-type equations and a change-of-variable formula in the spirit of Freidlin-Sheu for these so-called "Walsh semimartingales". We examine the solvability of the resulting system of stochastic integral equations. In appropriate Markovian settings we study two types of connections to martingale problems, questions of uniqueness in distribution for such processes, and a few examples.
8 citations
TL;DR: In this article, an elementary treatment of the Optional Decomposition Theorem for continuous semimartingales and general filtrations is presented, which does not assume the existence of equivalent local martingale measure(s), only that of strictly positive local Martingale deflator(s).
Abstract: We present an elementary treatment of the Optional Decomposition Theorem for continuous semimartingales and general filtrations. This treatment does not assume the existence of equivalent local martingale measure(s), only that of strictly positive local martingale deflator(s).
6 citations
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TL;DR: In this paper, an elementary treatment of the Optional Decomposition Theorem for continuous semimartingales and general filtrations is presented, which does not assume the existence of equivalent local martingale measure(s), only that of strictly positive local Martingale deflator(s).
Abstract: We present an elementary treatment of the Optional Decomposition Theorem for continuous semimartingales and general filtrations. This treatment does not assume the existence of equivalent local martingale measure(s), only that of strictly positive local martingale deflator(s).
3 citations
TL;DR: In this article, a Bayes sequential impulse control problem for a diffusion whose drift has an unobservable parameter with a change point is solved via a change of probability measure which removes the drift, and the solution is expressed in terms of the solutions and the current values of a Markov process adapted to the observation filtration.
Abstract: This paper solves a Bayes sequential impulse control problem for a diffusion, whose drift has an unobservable parameter with a change point. The partially observed problem is reformulated into one with full observations, via a change of probability measure which removes the drift. The optimal impulse controls can be expressed in terms of the solutions and the current values of a Markov process adapted to the observation filtration. We shall illustrate the application of our results using the Longstaff–Schwartz algorithm for multiple optimal stopping times in a geometric Brownian motion stock price model with drift uncertainty.
2 citations