Michael R. Powers

A theory of risk, return and solvency

Abstract In recent years, state regulators and state and federal lawmakers in the United States have become increasingly concerned with issues involving both the price and solvency regulation of insurers. In this article, we develop a risk-theoretic framework for studying both rate of return and solvency issues. Employing a certain class of diffusion processes to model insurer net worth, we use the expected discounted cost of insolvency (EDCI), a generalization of the probability of ruin, in constructing the regulators objective function. This objective function is then used to solve for the optimal rate of return and the optimal loss-to-net worth ratio.

Using Aumann-Shapley Values to Allocate Insurance Risk

Abstract The problem of allocating responsibility for risk among members of a portfolio arises in a variety of financial and risk-management contexts. Examples are particularly prominent in the insurance sector, where actuaries have long sought methods for distributing capital (net worth) across a number of distinct exposure units or accounts according to their relative contributions to the total “risk” of an insurer’s portfolio. Although substantial work has been done on this problem, no satisfactory solution has yet been presented for the case of inhomogeneous loss distributions— that is, losses X ∼ F X| λ such that F X|tλ (X) ≠ F tX| λ (X) for some t > 0. The purpose of this article is to show that the value-assignment method of nonatomic cooperative games proposed in 1974 by Aumann and Shapley may be used to solve risk-allocation problems involving losses of this type. This technique is illustrated by providing analytical solutions for a useful class of multivariatenormal loss distributions.

Insurance market games: Scale effects and public policy

We propose a game-theoretic model to study various effects of scale in an insurance market. After reviewing a simple static model of insurer solvency (in which all customers have inelastic demand), we present a one-period game in which both the buyers and sellers of insurance make strategic bids to determine market price and quantity. For the case in which both buyers and sellers are characterized by constant absolute risk aversion, we show that a unique market equilibrium exists under certain conditions. For the special case of risk-neutral insurers, we then consider how both the price and quantity of insurance, as well as other quantities of interest to public-policy decision makers, are affected by the number of insurance firms, the number of customers, and the total amount of capital provided by investors.

On the tradeoff between the law of large numbers and oligopoly in insurance

Abstract For a fixed number of customers in an insurance market, changing the number of insurance firms creates both scale effects on the individual firms (as the number of customers per firm is altered), and an oligopolistic effect on market supply. The most prominent effect of scale is the impact on solvency associated with the law of large numbers (LLN). In this paper, we focus on the relationship between the LLN and the oligopolistic effect of the number of firms in the market, and use a game-theoretic model of insurance market equilibrium to study this problem. For constant absolute risk averse buyers and risk neutral sellers, we find that there is a natural tradeoff between the effects of the LLN and oligopoly that causes both equilibrium quantity and the equilibrium payoff to customers to possess unique interior maxima over the number of insurance firms.

Equity in Automobile Insurance: Optional No-Fault

Throughout the past decade, automobile insurance premiums have escalated in many jurisdictions. Excessive litigation and the over-utilization of medical services have been primary forces pushing the price of automobile insurance beyond the reach of many consumers. Nationally, automobile insurance premiums increased an average of 9.6 percent annually, about three times the average rate of increase in the Consumer Price Index, from 1982 through 1988 (see A. M. Best Company, 1990). In Pennsylvania, where major automobile insurance reform has been enacted recently, the rate of increase was almost identical to the national average during this period of time.

Life-Insurance Efficiency in China: A Comparison of Foreign and Domestic Firms

The Chinese life-insurance industry has experienced major structural changes in recent years, primarily because of increasing demand and the entry of foreign insurers. Although the market is clearly booming, the efficiency of its growth and development is unclear. In this paper, we evaluate the efficiency of life insurers operating in China and compare foreign firms with domestic firms. We find that foreign insurers have not brought efficiency into the Chinese market, and that the market is still dominated by domestic giants. However, the gap between foreign insurers and domestic insurers is narrowing. After testing hypotheses regarding scale economy, technical progress and potential improvements, we discuss several issues of importance to life insurers, market investors and government regulators.

Toward a Theory of Reinsurance and Retrocession

There is a natural tradeoff between the benefits of increasing the number of competitors in an insurance market and the drawback to the weakening of the law of large numbers due to the diminishing of average reserves. In this investigation we consider the possibility for optimal layers of reinsurance and retrocession in the design of the insurance industry. A general question which may be asked of all financial institutions is what factors limit the number of layers of paper which can be constructed?

Risk finance for catastrophe losses with Pareto-calibrated Lévy-stable severities.

For catastrophe losses, the conventional risk finance paradigm of enterprise risk management identifies transfer, as opposed to pooling or avoidance, as the preferred solution. However, this analysis does not necessarily account for differences between light- and heavy-tailed characteristics of loss portfolios. Of particular concern are the decreasing benefits of diversification (through pooling) as the tails of severity distributions become heavier. In the present article, we study a loss portfolio characterized by nonstochastic frequency and a class of Lévy-stable severity distributions calibrated to match the parameters of the Pareto II distribution. We then propose a conservative risk finance paradigm that can be used to prepare the firm for worst-case scenarios with regard to both (1) the firms intrinsic sensitivity to risk and (2) the heaviness of the severitys tail.

Presbyter takes Knight

Purpose - The purpose of this editorial is to explore the usefulness of distinguishing between “risk” and “Knightian uncertainty.” Design/methodology/approach - The paper presents a representative, insurance-based model of Knightian uncertainty arising out of potential major structural changes (without historical precedent) in liability claim settlements. It then considers whether or not formal statistical forecasting and decision making are possible in this context. Findings - For real-world settings, it is found that a Bayesian statistical framework is sufficiently comprehensive to permit forecasting and decision making in the presence of Knightian uncertainty. The paper then shows that the Bayesian approach fails only if the sample space underlying the potential structural change is truly nonmeasurable. Originality/value - It is argued that, under a Bayesian worldview, the distinction between risk and uncertainty is necessary only in highly abstract epistemological modeling.

Thoughts on the “scientific method”: part 2 – frequentist fecklessness

Purpose - The purpose of this two-part series is to consider the role of the “scientific method” (SM) in human understanding, questioning both its consistency in actual practice and its reasonableness as a system of philosophy and action. Design/methodology/approach - Part 2 considers problems of inefficiency and inertia caused by the SMs collectivist, frequentist orientation. Findings - It is argued that problems caused by the SMs frequentist framework may be avoided by a more individualist, Bayesian approach. Originality/value - The two-part series challenges certain aspects of the “scientific method” as employed in the practice of modern science.