Mathematics 2022, 10, 2668. https://doi.org/10.3390/math10152668 www.mdpi.com/journal/mathematics Review Application of Compound Poisson Process in Pricing Catastrophe Bonds: A Systematic Literature Review Sukono 1, *, Hafizan Juahir 2 , Riza Andrian Ibrahim 3 , Moch Panji Agung Saputra 3 , Yuyun Hidayat 4 and Igif Gimin Prihanto 5 1 Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jatinangor 45363, Indonesia 2 East Coast Environmental Research Institute (ESERI), Universiti Sultan Zainal Abidin, Kuala Terengganu 21300, Malaysia; hafizanjuahir@unisza.edu.my 3 Doctoral Program, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jatinangor 45363, Indonesia; riza17005@mail.unpad.ac.id (R.A.I.); moch16006@mail.unpad.ac.id (M.P.A.S.) 4 Department of Statistics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Bandung 45363, Indonesia; yuyun.hidayat@unpad.ac.id 5 Research Center for Testing Technology and Standards, National Research and Innovation Agency, Jakarta Pusat 10340, Indonesia; igif001@brin.go.id * Correspondence: sukono@unpad.ac.id Abstract: The compound Poisson process (CPP) is often used in catastrophe risk modeling, for ex‐ ample, aggregate loss risk modeling. Hence, CPP can be involved in pricing catastrophe bonds (CAT bonds) because it requires a catastrophe risk modeling method. However, studies of how the appli‐ cation of CPP in pricing CAT bonds is still scarce. Therefore, this study aims to conduct a systematic literature review (SLR) on how CPP is used in pricing CAT bonds. The SLR consists of three stages: the literature selection, bibliometric analysis, and gap analysis. At the literature selection stage, the 30 articles regarding the application of CPP in pricing CAT bonds are obtained. Then, the conceptual and nonconceptual structures of the articles are mapped at the bibliometric analysis stage. Finally, in the gap analysis stage, the application of CPP in pricing CAT bonds from the previous studies is analyzed, and new research opportunities are studied. This research can be a reference for research‐ ers regarding the application of CPP in pricing CAT bonds and can motivate them to design more beneficial ways of pricing CAT bonds with CPP in the future. Keywords: compound Poisson process; catastrophe bond; pricing; systematic literature review; bibliometric analysis; gap analysis MSC: 60G55; 62P05; 91G20 1. Introduction The frequency of catastrophic events has experienced an increasing trend in almost all countries worldwide in the last five decades. This trend occurs for various catastro‐ phes, such as wildfires, droughts, earthquakes, extreme weather, floods, landslides, storms, and volcanoes. This increasing trend for each catastrophe in the last five decades can be seen in Figure 1 (source: https://www.emdat.be) (accessed on 15 May 2020). Figure 1 shows that the occurrence frequency of each catastrophe each year is around the increas‐ ing trend line. The increasing trend in catastrophic world events certainly causes a rising trend in economic losses. The World Meteorological Organization states that the economic loss from weather and climate catastrophes in 2010 alone was seven times that of 1970 [1], let alone the total economic loss for all types of catastrophes. Furthermore, this increasing Citation: Sukono; Juahir, H.; Ibrahim, R.A.; Saputra, M.P.A.; Hidayat, Y.; Prihanto, I.G. Application of Compound Poisson Process in Pricing Catastrophe Bonds: A Systematic Literature Review. Mathematics 2022, 10, 2668. https://doi.org/10.3390/ math10152668 Academic Editor: Christophe Chesneau Received: 4 July 2022 Accepted: 27 July 2022 Published: 28 July 2022 Publisher’s Note: MDPI stays neu‐ tral with regard to jurisdictional claims in published maps and institu‐ tional affiliations. Copyright: © 2022 by the author. Li‐ censee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and con‐ ditions of the Creative Commons At‐ tribution (CC BY) license (https://cre‐ ativecommons.org/licenses/by/4.0/).