Capital allocation and risk management in insurance

In this thesis, we mainly consider the risk analysis and capital allocation problem in the field of insurance. As a basic foundation of my PhD study, we propose a holistic principle in the first part to solve typical risk aggregation and capital allocation problem. In the classical framework, we observe three major pitfalls, namely lack of consistency, negligence of cost of capital, and disentanglement of allocated capitals from standalone capitals. With the help of the proposed one-single step holistic principle, we achieve a balance of optimality by taking into account competing interests of various stakeholders and conflicting priorities in a corporate hierarchy. While unconventional in its objective, the holistic principle also results in an allocation of diversification benefit, which conforms to the diversification strategy of many risk management frameworks including regulatory capital and economic capital. While in the second part, we study three different risks in insurance, namely investment risk in variable annuity, inflation risk in inflation-linked annuity, and pandemic risk in health insurance. The purpose of the risk analysis would be providing insights to the public, optimizing the existing frameworks, and helping insurers manage their collected premiums in an effective way. In the first work, we model the policyholder's and insurer's investment and mortality risks in guaranteed variable annuities. The intrinsic risk transfer and absorption mechanism are examined and we conclude that the policyholder gives up potential upside gain in exchange of protection from the downside loss. In the second work, with the help of Jarrow-Yildirim model, we propose an inflation-linked annuity in which the benefit payments are modified by the change of inflation indexation. We propose the pricing formula and construct an efficient dynamic hedging strategy, in which the hedging portfolio achieves a low hedging error in our numerical illustration. In the last work, we explore the epidemiology literature and adopt an infection-age model to capture the transmission dynamics. We then use these models to determine the cost and reserve for healthcare insurer. Compared to classical life insurance, healthcare insurer's reserve function exhibits different patterns over the course of pandemic and so we formulate conditions under which various reserve shapes arise. Moreover, inspired by well-known loss reserving techniques, we introduce a loss triangle to predict future unpaid healthcare liabilities during a pandemic.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Jin, Longhao

Contributors dc:contributor

• Feng, Runhuan
• Feng, Liming
• Quan, Zhiyu
• Chong, Wing Fung

• Capital allocation
• Risk aggregation
• Holistic principle
• Loss Triangle
• Infection-age model

Statement dc:rights

• Copyright 2022 Longhao Jin

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/115371

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F115371