Macrina, A;
Sekine, J;
(2021)
Stochastic modelling with randomized Markov bridges.
Stochastics
, 93
(1)
pp. 29-55.
10.1080/17442508.2019.1703988.
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Abstract
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, governing 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 observation 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 diffusion bridge and show how it can be utilized to extend well-known commodity pricing models and how one may propose novel stochastic price models for financial instruments linked to greenhouse gas emissions.
| Type: | Article |
|---|---|
| Title: | Stochastic modelling with randomized Markov bridges |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1080/17442508.2019.1703988 |
| Publisher version: | https://doi.org/10.1080/17442508.2019.1703988 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Randomized Markov bridge, hidden random variable, filtering, skew-normal randomized diffusion, commodity pricing, greenhouse gas emission, climate risk management |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10088903 |
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