Filters

20132

More filters

20192
Reset filters

Settings

Author: Bayer, Christian × Subject: Monte Carlo simulation ×

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Forward-reverse EM algorithm for Markov chains
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Bayer, Christian; Mai, Hilmar; Schoenmakers, John G.M.
    We develop an EM algorithm for estimating parameters that determine the dynamics of a discrete time Markov chain evolving through a certain measurable state space. As a key tool for the construction of the EM method we develop forward-reverse representations for Markov chains conditioned on a certain terminal state. These representations may be considered as an extension of the earlier work [1] on conditional diffusions. We present several experiments and consider the convergence of the new EM algorithm.
  • Thumbnail Image
    Item
    Simulation of conditional diffusions via forward-reverse stochastic representations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Bayer, Christian; Schoenmakers, John G.M.
    In this paper we derive stochastic representations for the finite dimensional distributions of a multidimensional diffusion on a fixed time interval, conditioned on the terminal state. The conditioning can be with respect to a fixed point or more generally with respect to some subset. The representations rely on a reverse process connected with the given (forward) diffusion as introduced in Milstein et al. [Bernoulli 10(2):281312, 2004] in the context of a forward-reverse transition density estimator. The corresponding Monte Carlo estimators have essentially root-N accuracy, hence they do not suffer from the curse of dimensionality. We provide a detailed convergence analysis and give a numerical example involving the realized variance in a stochastic volatility asset model conditioned on a fixed terminal value of the asset.