Now showing items 1-20 of 21

    • A jump telegraph model for option pricing 

      Ratanov, Nikita
      In this paper we introduce a financial market model based on continuos time random motions with alternanting constant velocities and with jumps ocurring when the velocity switches. if jump directions are in the certain ...
       Documento de trabajo. 2004
    • A two-state neuronal model with alternating exponential excitation 

      Ratanov, Nikita
      We develop a stochastic neural model based on point excitatory inputs. The nerve cell depolarisation is determined by a two-state point process corresponding the two states of the cell. The model presumes state-dependent ...
       Artículo. 2019
    • Branching random motions, nonlinear hyperbolic systems and traveling waves 

      Ratanov, Nikita
      A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independient of random motion, and intensities of reverses are defined by a particle's current direction. A ...
       Documento de trabajo. 2004
    • Branching random motions, nonlinear hyperbolic systems and travelling waves 

      Ratanov, Nikita
      A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independent of random motion, and intensities of reverses are defined by a particle’s current direction. A ...
       Artículo. 2006
    • Damped jump-telegraph processes 

      Ratanov, Nikita
      We study a one-dimensional Markov modulated random walk with jumps. It is assumed that the amplitudes of the jumps as well as the chosen velocity regime are random, and depend on the time spent by the process at the previous ...
       Artículo. 2013
    • Double Telegraph Processes and Complete Market Models 

      Ratanov, Nikita
      The traditional jump-telegraph processes are based on a Poisson process with alternating intensities. We develop a new model based on an alternating doubly stochastic Poisson process with random intensities of jumps. ...
       Artículo. 2014
    • First Crossing Times of Telegraph Processes with Jumps 

      Ratanov, Nikita
      The paper presents exact formulae related to the distribution of the first passage time ?x of the jump-telegraph process. In particular, the Laplace transform of ?x is analysed, when a jump component is in the opposite ...
       Artículo. 2020
    • Hypo-exponential distributions and compound Poisson processes with alternating parameters 

      Ratanov, Nikita
      Point processes with alternating arrival rates arise in various applications, including financial modelling. We obtain explicit expressions for the distributions of these processes, i.e. for the sums ?m=1nX(m) and ...
       Artículo. 2015
    • Jump telegraph processes and financial markets with memory 

      Ratanov, Nikita
      The paper develops a new class of financial market models. These models are based on generalized telegraph processes with alternating velocities and jumps occurring at switching velocities. The model under consideration ...
       Artículo. 2007
    • Kac's rescaling for jump-telegraph processes 

      López, Oscar; Ratanov, Nikita
      We present limit theorems for an asymmetric telegraph process with drift and jumps under different rescaling conditions. The explicit formulae for the related characteristic functions are derived by solving a Cauchy problem ...
       Artículo. 2012
    • Kac–Lévy Processes 

      Ratanov, Nikita
      Markov-modulated Lévy processes with two different regimes of restarting are studied. These regimes correspond to the completely renewed process and to the process of Markov modulation, accompanied by jumps. We give explicit ...
       Artículo. 2020
    • Occupation time distributions for the telegraph process 

      Bogachev, Leonid; Ratanov, Nikita
      For the one-dimensional telegraph process, we obtain explicitly the distribution of the occupation time of the positive half-line. The long-term limiting distribution is then derived when the initial location of the process ...
       Artículo. 2011
    • On financial markets based on telegraph processes 

      Ratanov, Nikita; Melnikov, Alexander
      "The paper develops a new class of financial market models. These models are based on generalised telegraph processes: Markov random flows with alternating velocities and jumps occurring when the velocities are switching. ...
       Artículo. 2008
    • On piecewise linear processes 

      Ratanov, Nikita
      The letter concerns piecewise deterministic processes controlled by a Markov flow with exponentially, Exp (?n), distributed interarrival times T n. Assuming all rates ?n to be different, we study the distribution of a ...
       Artículo. 2014
    • On the asymmetric telegraph processes 

      López, Oscar; Ratanov, Nikita
      "We study the one-dimensional random motionX = X(t), t 0, which takes two different velocities with two different alternating intensities. The closed-form formulae for the density functions of X and for the moments of any ...
       Artículo. 2014
    • Option pricing driven by a telegraph process with random jumps 

      López, Oscar; Ratanov, Nikita
      "In this paper we propose a class of financial market models which are based on telegraph processes with alternating tendencies and jumps. It is assumed that the jumps have random sizes and that they occur when the tendencies ...
       Artículo. 2012
    • Option pricing model based on telegraph processes with jumps 

      Ratanov, Nikita
      En este artículo superamos las carencias del modelo de Black-Scholes, es decir, la velocidad de propagación infinita, los precios de los activos infinitamente grandes, etc. El modelo propuesto se basa en el proceso telegráfico ...
       Documento de trabajo. 2004
    • Quantil Hedging for telegraph markets and its applications to a pricing of equity-linked life insurance contracts 

      Ratanov, Nikita
      En este documento está desarrollado un modelo de mercado financiero basado en movimientos aleatorios con tiempo continuo, con velocidades constantes alternantes y saltos cuando hay cambios en la velocidad. Si los saltos ...
       Documento de trabajo. 2005
    • Self-exciting piecewise linear processes 

      Ratanov, Nikita
      The paper concerns a piecewise linear process controlled by the set of velocities {cn}n≥0 consecutively switched after exponentially distributed, Exp(λn), n ≥ 0, time intervals. The distribution of such process is studied ...
       Artículo. 2017
    • Telegraph models of financial markets 

      Ratanov, Nikita
      En este artículo introducimos un modelo de mercado financiero basado en movimientos aleatorios con la alternancia de velocidades y con saltos que ocurren cuando la velocidad se cambia. Este modelo es libre del arbitraje ...
       Artículo. 2001