Optimal Reinsurance for the Solvency of Automobile Portfolio: Application to Sub-Saharan Africa
Abstract
This paper examines actuarial strategies to maintain the solvency of automobile insurance portfolios in sub-Saharan Africa, where motor insurance is mandatory and a significant revenue source, representing approximately 60% of total premiums in the CIMA (the Inter-African Conference on Insurance Markets) region. Poorly managed auto insurance portfolios risk pushing insurers toward insolvency, necessitating proactive financial measures. The study evaluates a priori and a posteriori pricing methods, concluding that neither approach alone sufficiently mitigates solvency risks due to the portfolio's heterogeneity and the potential for premium default. Our proposed solution, surplus share reinsurance, is a proportional and individualized strategy in which the insurer sets a retention limit per policy, only retaining premiums below this threshold. Additionally, establishing a reserve fund is essential to cover any potential shortfalls. The probability of ruin, assessed through a random walk analysis of risk reserves, is vital for evaluating the portfolio’s financial stability and guiding risk management decisions.
Keywords: priori pricing; full surplus reinsurance; thirst for insurance bonuses; bonus-malus system; line-by-line provisioning.
Abstrak
Artikel ini mengkaji strategi aktuaria untuk mempertahankan solvabilitas portofolio asuransi mobil di Afrika sub-Sahara, dimana asuransi kendaraan bermotor bersifat wajib dan merupakan sumber pendapatan yang signifikan, yang mewakili sekitar 60% dari total premi di kawasan CIMA (Konferensi Antar-Afrika tentang Pasar Asuransi). Portofolio asuransi kendaraan bermotor yang dikelola dengan buruk berisiko mendorong perusahaan asuransi menuju kebangkrutan, sehingga memerlukan langkah-langkah keuangan yang proaktif. Studi ini mengevaluasi metode penetapan harga apriori dan a posteriori, dan menyimpulkan bahwa tidak satu pun pendekatan yang cukup memitigasi risiko solvabilitas karena heterogenitas portofolio dan potensi gagal bayar premi. Solusi yang kami usulkan, reasuransi surplus share, adalah strategi proporsional dan individual di mana perusahaan asuransi menetapkan batas retensi per polis, hanya menahan premi di bawah ambang batas ini. Selain itu, pembentukan dana cadangan sangat penting untuk menutupi potensi kekurangan. Peluang kebangkrutan, yang dinilai melalui analisis random walk dari cadangan risiko, sangat penting untuk mengevaluasi stabilitas keuangan portofolio dan memandu keputusan manajemen risiko.
Kata Kunci: penetapan harga apriori; reasuransi surplus penuh; kehausan akan bonus asuransi; sistem bonus-malus; provisi lini per lini.
2020MSC: 62P05, 91G05.
Keywords
References
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DOI: 10.15408/inprime.v6i2.38325
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