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2 results

  • The Markov Chain Market

  • Ragnar Norberg
  • Journal:
    ASTIN Bulletin: The Journal of the IAA / Volume 33 / Issue 2 / November 2003
    Published online by Cambridge University Press:
    17 April 2015, pp. 265-287
    Print publication:
    November 2003
    • Article
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  • We consider a financial market driven by a continuous time homogeneous Markov chain. Conditions for absence of arbitrage and for completeness are spelled out, non-arbitrage pricing of derivatives is discussed, and details are worked out for some cases. Closed form expressions are obtained for interest rate derivatives. Computations typically amount to solving a set of first order partial differential equations. An excursion into risk minimization in the incomplete case illustrates the matrix techniques that are instrumental in the model.

  • On branching processes allowing immigration

  • Y. S. Yang
  • Journal:
    Journal of Applied Probability / Volume 9 / Issue 1 / March 1972
    Published online by Cambridge University Press:
    14 July 2016, pp. 24-31
    Print publication:
    March 1972

  • Continuous time one-type branching processes allowing immigration are considered. The invariant measure, which is shown to be unique, is exhibited. From this, a condition for positive recurrence similar to that of Heathcote's in the discrete time case is obtained. For the critical discrete time case, Seneta's sufficient condition for positive recurrence is improved to give a necessary and sufficient condition.