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Open AccessArticle

Discrete-Time Risk Models with Claim Correlated Premiums in a Markovian Environment

by and *,†
Department of Economics, The University of Melbourne, Parkville, VIC 3010, Australia
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Risks 2021, 9(1), 26; https://doi.org/10.3390/risks9010026
Received: 18 November 2020 / Revised: 7 January 2021 / Accepted: 10 January 2021 / Published: 14 January 2021
In this paper we consider a discrete-time risk model, which allows the premium to be adjusted according to claims experience. This model is inspired by the well-known bonus-malus system in the non-life insurance industry. Two strategies of adjusting periodic premiums are considered: aggregate claims or claim frequency. Recursive formulae are derived to compute the finite-time ruin probabilities, and Lundberg-type upper bounds are also derived to evaluate the ultimate-time ruin probabilities. In addition, we extend the risk model by considering an external Markovian environment in which the claims distributions are governed by an external Markov process so that the periodic premium adjustments vary when the external environment state changes. We then study the joint distribution of premium level and environment state at ruin given ruin occurs. Two numerical examples are provided at the end of this paper to illustrate the impact of the initial external environment state, the initial premium level and the initial surplus on the ruin probability. View Full-Text
Keywords: discrete-time risk model; bonus-malus system; Markov modulated risk model; finite-time ruin; recursive computation; Lundberg inequality discrete-time risk model; bonus-malus system; Markov modulated risk model; finite-time ruin; recursive computation; Lundberg inequality
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MDPI and ACS Style

Osatakul, D.; Wu, X. Discrete-Time Risk Models with Claim Correlated Premiums in a Markovian Environment. Risks 2021, 9, 26. https://doi.org/10.3390/risks9010026

AMA Style

Osatakul D, Wu X. Discrete-Time Risk Models with Claim Correlated Premiums in a Markovian Environment. Risks. 2021; 9(1):26. https://doi.org/10.3390/risks9010026

Chicago/Turabian Style

Osatakul, Dhiti; Wu, Xueyuan. 2021. "Discrete-Time Risk Models with Claim Correlated Premiums in a Markovian Environment" Risks 9, no. 1: 26. https://doi.org/10.3390/risks9010026

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