2020年度

Math-Fi seminar on 4 Jun.

2020.06.04 Thu up
  • Date: 4 Jun.  (Thu.)
  • Place: On the Web
  • Time: 16:30-18:00
  • Speaker: Guanting Liu (UNSW)
  • Title: A positivity-preserving numerical scheme for the alpha-CEV process
  • Abstract: 
​We propose and prove strong convergence of a positivity-preserving implicit numerical scheme for jump-extended Cox-Ingersoll-Ross (CIR) process and Constant-Elasticity-of-Variance (CEV) process, where the jumps are governed by a compensated spectrally positive alpha-stable Levy process for alpha in (1, 2).
This class of models have first been studied in the context of continuous branching processes with interaction and/or immigration, and in this class a model has been introduced to mathematical finance for modelling sovereign interest rates and the energy market, which was named the alpha-CIR process. Numerical schemes for jump-extended CIR and CEV processes in the current literature, to the best of our knowledge, have all focused on the case of finite activity jumps (e.g. Poisson jumps) except our previous work studying a positivity-preserving scheme for the alpha-CIR process. In this paper, besides strong convergence we also obtain bounded beta-moments of the numerical scheme, for beta in [1, alpha), which allows us to left the boundedness requirement on the jump coefficient, and hence avoid truncation.
 

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