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Log-optimal investment in the long run with proportional transaction costs when using shadow prices

Petr Dostál, Jana Klůjová (2015)

Kybernetika

We consider a non-consuming agent interested in the maximization of the long-run growth rate of a wealth process investing either in a money market and in one risky asset following a geometric Brownian motion or in futures following an arithmetic Brownian motion. The agent faces proportional transaction costs, and similarly as in [17] where the case of stock trading is considered, we show how the log-optimal optimal policies in the long run can be derived when using the technical tool of shadow...

Long memory and self-similar processes

Gennady Samorodnitsky (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

This paper is a survey of both classical and new results and ideas on long memory, scaling and self-similarity, both in the light-tailed and heavy-tailed cases.

Long time behavior of random walks on abelian groups

Alexander Bendikov, Barbara Bobikau (2010)

Colloquium Mathematicae

Let be a locally compact non-compact metric group. Assuming that is abelian we construct symmetric aperiodic random walks on with probabilities n ↦ ℙ ( S 2 n ∈ V ) of return to any neighborhood V of the neutral element decaying at infinity almost as fast as the exponential function n ↦ exp(-n). We also show that for some discrete groups , the decay of the function n ↦ ℙ ( S 2 n ∈ V ) can be made as slow as possible by choosing appropriate aperiodic random walks Sₙ on .

Long time behaviour and stationary regime of memory gradient diffusions

Sébastien Gadat, Fabien Panloup (2014)

Annales de l'I.H.P. Probabilités et statistiques

In this paper, we are interested in a diffusion process based on a gradient descent. The process is non Markov and has a memory term which is built as a weighted average of the drift term all along the past of the trajectory. For this type of diffusion, we study the long time behaviour of the process in terms of the memory. We exhibit some conditions for the long-time stability of the dynamical system and then provide, when stable, some convergence properties of the occupation measures and of the...

Long-range self-avoiding walk converges to α-stable processes

Markus Heydenreich (2011)

Annales de l'I.H.P. Probabilités et statistiques

We consider a long-range version of self-avoiding walk in dimension d > 2(α ∧ 2), where d denotes dimension and α the power-law decay exponent of the coupling function. Under appropriate scaling we prove convergence to brownian motion for α ≥ 2, and to α-stable Lévy motion for α < 2. This complements results by Slade [J. Phys. A21 (1988) L417–L420], who proves convergence to brownian motion for nearest-neighbor self-avoiding walk in high dimension.

Loop-free Markov chains as determinantal point processes

Alexei Borodin (2008)

Annales de l'I.H.P. Probabilités et statistiques

We show that any loop-free Markov chain on a discrete space can be viewed as a determinantal point process. As an application, we prove central limit theorems for the number of particles in a window for renewal processes and Markov renewal processes with Bernoulli noise.

Currently displaying 161 – 180 of 182