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  • 1.
    Andreev, Andriy
    et al.
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Morlanes, José Igor
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Simulations-based Study of Covariance Structure for Fractional Ornstein-Uhlenbeck process of the Second KindManuskript (preprint) (Annet vitenskapelig)
  • 2. Azmoodeh, Ehsan
    et al.
    Morlanes, José Igor
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Drift parameter estimation for fractional Ornstein-Uhlenbeck process of the second kind2015Inngår i: Statistics (Berlin), ISSN 0233-1888, E-ISSN 1029-4910, Vol. 49, nr 1, s. 1-18Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The fractional Ornstein-Uhlenbeck process of the second kind (fOU(2)) is the solution of the Langevin equation <inline-graphic xmlns:xlink=http://www.w3.org/1999/xlink xlink:href=gsta_a_863888_ilm0001.gif></inline-graphic> with driving noise <inline-graphic xmlns:xlink=http://www.w3.org/1999/xlink xlink:href=gsta_a_863888_ilm0002.gif></inline-graphic> where B is a fractional Brownian motion with Hurst parameter H(0, 1). In this article, in the case H>1/2, we prove that the least-squares estimator <inline-graphic xmlns:xlink=http://www.w3.org/1999/xlink xlink:href=gsta_a_863888_ilm0003.gif></inline-graphic> introduced in [Hu Y, Nualart D. Parameter estimation for fractional Ornstein-Uhlenbeck processes. Stat. Probab. Lett. 2010;80(11-12):1030-1038], provides a consistent estimator. Moreover, using central limit theorem for multiple Wiener integrals, we prove asymptotic normality of the estimator valid for the whole range H(1/2, 1).

  • 3. Gasbarra, Dario
    et al.
    Morlanes, José Igor
    Aalto University, Finland.
    Valkeila, Esko
    Initial Enlargement in a Markov Chain Market Model2011Inngår i: Stochastics and Dynamics, ISSN 0219-4937, Vol. 11, nr 2-3, s. 389-413Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Enlargement of filtrations is a classical topic in the general theory of stochastic processes. This theory has been applied to stochastic finance in order to analyze models with insider information. In this paper we study initial enlargement in a Markov chain market model, introduced by Norberg. In the enlarged filtration, several things can happen: some of the jumps times can be accessible or predictable, but in the original filtration all the jumps times are totally inaccessible. But even if the jumps times change to accessible or predictable, the insider does not necessarily have arbitrage possibilities. Read More: http://www.worldscientific.com/doi/abs/10.1142/S021949371100336X

  • 4.
    Morlanes, José Igor
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Some Extensions of Fractional Ornstein-Uhlenbeck Model: Arbitrage and Other Applications2017Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    This doctoral thesis endeavors to extend probability and statistical models using stochastic differential equations. The described models capture essential features from data that are not explained by classical diffusion models driven by Brownian motion.

    New results obtained by the author are presented in five articles. These are divided into two parts. The first part involves three articles on statistical inference and simulation of a family of processes related to fractional Brownian motion and Ornstein-Uhlenbeck process, the so-called fractional Ornstein-Uhlenbeck process of the second kind (fOU2). In two of the articles, we show how to simulate fOU2 by means of circulant embedding method and memoryless transformations. In the other one, we construct a least squares consistent estimator of the drift parameter and prove the central limit theorem using techniques from Stochastic Calculus for Gaussian processes and Malliavin Calculus.

    The second phase of my research consists of two articles about jump market models and arbitrage portfolio strategies for an insider trader. One of the articles describes two arbitrage free markets according to their risk neutral valuation formula and an arbitrage strategy by switching the markets. The key aspect is the difference in volatility between the markets. Statistical evidence of this situation is shown from a sequential data set. In the other one, we analyze the arbitrage strategies of an strong insider in a pure jump Markov chain financial market by means of a likelihood process. This is constructed in an enlarged filtration using Itô calculus and general theory of stochastic processes.

  • 5.
    Morlanes, José Igor
    et al.
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Andreev, Andriy
    Stockholms universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
    Simulation of fractional Ornstein-Uhlenbeck of the second kind by Circulant Embedding method2017Konferansepaper (Fagfellevurdert)
  • 6.
    Morlanes, José Igor
    et al.
    Aalto University, Finland.
    Rasila, Antti
    Sottinen, Tommi
    Empirical Evidence on arbitrage by changing the stock exchange2009Inngår i: Advances and Applications in Statistics, ISSN 0972-3617, Vol. 12, nr 2, s. 223-233Artikkel i tidsskrift (Fagfellevurdert)
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