Optimal Reciprocal Reinsurance under VaR or TVaR Constraint

Most existing researches on optimal reinsurance contract are based on an insurer’s viewpoint. However, the optimal reinsurance contract for an insurer is not necessarily to be optimal for a reinsurer. Hence, this study aims to develop the optimal reciprocal reinsurance which satisfies the benefits of both the insurer and reinsurer. Additionally, due to legislative restriction or risk management requirement, the wealth of insurer and reinsurer are frequently imposed upon a VaR (Value-at-Risk) or TVaR (Tail Value-at-Risk) constraint. Therefore, this study develops an optimal reciprocal reinsurance contract which maximizes the common benefits (evaluated by weighted addition of expected utilities) of the insurer and reinsurer subject to their VaR or TVaR constraints. Furthermore, for avoiding moral hazard problem, the developed contract is additionally restricted to a regular form or incentive compatibility (both indemnity schedule and retained loss schedule are continuously nondecreasing).

Bounded, Sigmoid Utility for Insurance Applications

Applying a well-known argument of Karl Menger to an insurance version of the St. Petersburg Paradox (in which the decision maker is confronted with losses, rather than gains), one can assert that von Neumann-Morgenstern utility functions are necessarily concave upward and bounded below as decision-maker wealth tends to negative infinity. However, this argument is subject to two potential criticisms: (1) infinite-mean losses do not exist in the real world; and (2) the St. Petersburg Paradox derives its force from empirical observation (i. e., that actual decision makers would not agree to an arbitrarily large insurance bid price to transfer an infinite-mean loss), and thus does not impart logical necessity. In the present article, these two criticisms are addressed in turn. We first show that, although infinite-mean insurance losses technically do not exist, they do provide a reasonable model for certain large (i. e., excess and reinsurance) property-liability indemnities. We then employ the Two-Envelope Paradox to demonstrate the logical necessity of concave-upward, lower-bounded utility for arbitrarily small (i. e., negative) values of wealth. Finally, we note that recognizing the bounded, sigmoid nature of utility functions challenges certain fundamental understandings in the economics of insurance demand, and can lead to vastly different conclusions regarding the bid price for insurance.

Dependency between Risks and the Insurer’s Economic Capital: A Copula-based GARCH Model

Copulas can be a useful tool to capture heavy-tailed dependence between risks in estimating economic capital. This paper provides a procedure of combining copula with GARCH model to construct a multivariate distribution. The copula-based GARCH model using a skewed student’s t-distribution controls for the issues of skewness, heavy tails, volatility clustering and conditional dependencies contained in the financial time series data. Using the sample of U.S. property liability insurance industry, we perform Monte Carlo simulation to estimate the insurer’s economic capital measured by Value-at-Risk (VaR) and Expected Shortfall (ES). The result indicates that the choice of dependence structure and business mix between asset classes and liability lines has a significant impact on the resulting capital requirements and diversification benefits. We find the incremental diversification benefit in terms of a reduction in the total capital requirement from the joint modeling of underwriting risk and market risk compared to the modeling of market risk only.

Longevity Risk-Sharing Annuities: Partial Indexation in Mortality Experience

In a conventional fixed annuity, idiosyncratic risk is diversified away while systematic longevity risk is borne entirely by the provider. The mortality-indexed annuity on the other hand, transfers systematic longevity risk completely back to the annuitants by fully adjusting benefits to mortality experience. In this paper, we propose the partial mortality-indexed annuity (PMIA), which aims to seek a balance between the two ends of the risk-sharing spectrum. Through a simulation study, we show that the PMIA achieves risk sharing and benefits both the provider and the annuitant.

Does Diversification Drive Down Risk-adjusted Returns? A Quantile Regression Approach

This study examines diversification-performance relationship in the U.S. property-liability insurance industry over the period of 1996–2010. Unlike prior studies that rely on the conditional mean estimation method, we employ quantile regression, which captures the heterogeneous effects of diversification on conditional return distribution. The results show that diversification does not necessarily drive down risk-adjusted returns and its effects vary along return distribution. We find that there is a diversification discount for firms in the lower levels of return distribution, whereas a diversification premium exists for firms in the upper levels of return distribution. We provide evidence that the relations between risk-adjusted returns and other explanatory variables are not constant, but vary over the quantiles of return distribution. Our results are robust to alternative measures of an insurer’s performance and product diversification.

An Investigation of Residential Insurance Demand-side Reactions After a Natural Catastrophe: The Case of the 2010–11 Christchurch Earthquakes

This study gives an empirical analysis of residential insurance demand-side reactions after an earthquake disaster using survey data. The paper discussed the study hypothesis from economic analysis perspective with significance econometric tests to explain how insurance demand for residential property changed post-catastrophe. Our empirical results observe higher risk perception from those who have had prior experience of catastrophes than those who have not. This positively influence the demand for residential insurance cover in the aftermath of a natural disaster with higher demand observed in the regions with higher seismic risk. These results support the research hypothesis and are consistent with the findings in our literature. A change in insurance level is less likely when the cost of the insurance is high, when the expected loss is low, and individuals becomes wealthier. We also find evidence of effects that remain to be explained, such as the greater sensitivity to both cost of insurance coverage and risk perception than to the size of the potential loss. We observe a positive relationship between household characteristics and the degree of risk aversion and how this changes with change in level of income, change in value of insured assets and change in insurance premiums. An increase in individual’s income alone has no major effect on insurance demand if the premium rates are within the demanders’ price range. However, positive loading of premiums to reflect transaction costs and possibility of adverse selection might affect insurance coverage level if premium rates become too high. In such cases, the direction of the effect depends on whether an increase in income increases both the premium rates and the insured asset and on whether the insurance demander has increasing or decreasing absolute risk aversion.

Econometrics Illustrated, with Applications from Insurance-Research Awards

The linear regression model is the dominant tool employed in applied risk and insurance research. Based on my 2016 APRIA lecture at Chengdu, China, I illustrate the simple geometry of the linear regression model, as well as some standard results from it: omitted variable bias (OVB), classical measurement error (CME), simultaneous equation models (SEM), and instrumental variable estimation. Instrumental variable estimation solves OVB, CME, and SEM problems by constructing similar triangles to retrieve consistent estimates. I apply these tools by estimating the determinants of the Witt and Mehr awards given annually for Journal of Risk and Insurance articles, as two examples. The Witt vs. Mehr awards also contrasts short-term scholarly recognition (Witt) versus long-term scholarly recognition (Mehr). The comments made here apply to other paper awards, such as those presented by the Asian Pacific Journal of Risk and Insurance. I also present a simple index function based on the classical Gini index (hence, this new index is denoted as the regression gini index, RGI) useful for comparing two regression models, and apply this to explain the empirical difference between the determinants of the Witt and Mehr awards.

Adjusting the Premium Relativities in a Bonus-Malus System: An Integrated Approach Using the First Claim Time and the Number of Claims

In this paper, we propose an integrated approach to adjust the premium relativities in a bonus-malus system by using the information of the first claim time (expressed in terms of sub-period in a year) and the number of claims reported by individual policyholder. We provide a formal representation for the newly proposed structure and derive the analytical expressions for the adjusted premium relativities. Other things being equal, a lower adjusted premium relativity is imposed for an earlier sub-period of the first claim made, whereas policyholders with more claims are subject to a higher adjusted premium relativity.

Extending Demographic Windows of Opportunity: Evidence from Asia

Population aging and a shrinking workforce creates a significant drag on opportunities for economic growth. Specifically, many economies in Asia will see their demographic windows of economic opportunity close within the next two decades or so. One widely explored policy response among governments has been to encourage longer working lives or delay retirement. This paper traces developments in retirement age policies for rapidly aging Asian economies, and investigates the effect of recent reforms in old-age employment practices on their demographic windows. We find that increases in retirement age based on current policy prescriptions can help these aging economies extend their demographic windows by another two to seven years. Nonetheless, further extensions to working lives are needed to help sustain economic expansion and to provide support for growing elderly populations. Our study also demonstrates that the extent of the time gains from retirement age increases vary depending on how the age structures in each economy is expected to evolve over time. Accordingly, the timing and quantum of future retirement age increases should be suitably calibrated so as to sufficiently offset declines in the working-age population.

Value Investing: Circle of Competence in the Thai Insurance Industry

This study explores the strategy of value investing, specifically for the insurance industry in Thailand. It employs multiple measures of “value,” suitable for insurance companies, such as the price-to-earning (PE), price-to-book (PB), and cyclically adjusted price-to-earnings (CAPE). Value premium exists in the Thai insurance industry, and most of the value portfolios constructed from these measures significantly outperform the market, even when adjusting for price volatility and portfolio’s