• Title, Summary, Keyword: compensated Poisson process

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Positive Interest Rate Model in the Presence of Jumps

  • Rhee, Joonhee;Kim, Yoon Tae
    • Communications for Statistical Applications and Methods
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    • v.11 no.3
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    • pp.495-501
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    • 2004
  • HJM representation of the term structure of interest rates sometimes produces the negative interest rates with positive probability. This paper shows that the condition of positive interest rates can be derived from the jump diffusion process, if a proper positive martingale process with the compensated jump process is chosen. As in Flesaker and Hughston, the condition is incorporated into the bond price process.

EULER-MARUYAMA METHOD FOR SOME NONLINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH JUMP-DIFFUSION

  • Ahmed, Hamdy M.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.18 no.1
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    • pp.43-50
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    • 2014
  • In this paper we discussed Euler-Maruyama method for stochastic differential equations with jump diffusion. We give a convergence result for Euler-Maruyama where the coefficients of the stochastic differential equation are locally Lipschitz and the pth moments of the exact and numerical solution are bounded for some p > 2.