UCL Discovery
UCL home » Library Services » Electronic resources » UCL Discovery

Stochastic modelling with randomized Markov bridges

Macrina, A; Sekine, J; (2021) Stochastic modelling with randomized Markov bridges. Stochastics , 93 (1) pp. 29-55. 10.1080/17442508.2019.1703988. Green open access

[thumbnail of RMB-MS2019DEC13 (1).pdf]
Preview
Text
RMB-MS2019DEC13 (1).pdf - Accepted Version

Download (787kB) | Preview

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.ucl.ac.uk/id/eprint/10088903
Downloads since deposit
78Downloads
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item