Journal article

Stochastic modelling with randomized Markov bridges

Publication Details

Author list: Macrina A, Sekine J

Publication year: 2021

Journal: Stochastics

Volume number: 93

Issue number: 1

Start page: 29

End page: 55

Total number of pages: 27

ISSN: 0090-9491



We consider the filtering problem of estimating a hidden random variable X by noisy
observations. The noisy observation process is constructed by a randomized Markov bridge
(RMB) (Zt)t [₀,T] of which terminal value is set to ZT X. That is, at the terminal time T,
the noise of the bridge process vanishes and the hidden random variable X is revealed. We derive
the explicit filtering formula, gov- erning the dynamics of the conditional probability
process, for a general RMB. It turns out that the conditional probability is given by a function
of current time t, the current observation Zt, the initial obser- vation Z₀, and the a priori
distribution ν of X at t 0. As an example for an RMB, we explicitly construct the skew-normal
randomized dif- fusion bridge and show how it can be utilized to extend well-known commodity
pricing models and how one may propose novel stochas- tic price models for financial instruments
linked to greenhouse gas emissions.

Received 15 September 2017
Accepted 10 December 2019

Randomized Markov bridge; hidden random variable; filtering; skew-normal randomized diffusion;
commodity pricing; greenhouse gas emission; climate risk management


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