16,321 research outputs found
Solutions of Backward Stochastic Differential Equations on Markov Chains
We consider backward stochastic differential equations (BSDEs) related to
finite state, continuous time Markov chains. We show that appropriate solutions
exist for arbitrary terminal conditions, and are unique up to sets of measure
zero. We do not require the generating functions to be monotonic, instead using
only an appropriate Lipschitz continuity condition.Comment: To appear in Communications on Stochastic Analysis, August 200
Filters and smoothers for self-exciting Markov modulated counting processes
We consider a self-exciting counting process, the parameters of which depend
on a hidden finite-state Markov chain. We derive the optimal filter and
smoother for the hidden chain based on observation of the jump process. This
filter is in closed form and is finite dimensional. We demonstrate the
performance of this filter both with simulated data, and by analysing the
`flash crash' of 6th May 2010 in this framework
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