Larry Y. Tzeng

Organizational Form in the Property-Liability Insurance Industry

INTRODUCTION Recent research has argued that alternative organizational forms will coexist in an industry because of differential relative advantages. (See, for example, Jensen and Meckling, 1976; Klein, Crawford, and Alchian, 1978; Fama and Jensen, 1983; Williamson, 1985.) The two important elements of organizational form are the ownership structure of the firm, and the degree to which the firm internalizes or outsources production, that is, the level of vertical integration. The property-liability insurance industry is characterized by firms that differ on both of these dimensions of organizational form. The range of ownership structures includes stock corporations, mutuals, and reciprocal organizations. Stockholder-owned insurers dominate the market, with 67.7 percent share of premiums written in 1994. Stock insurers controlled 55 percent of the personal lines market, which includes auto and homeowners insurance, but held a commanding lead in commercial lines, with a 79 percent share. Property-liability insurance firms also vary widely in the degree of vertical integration of the distribution system, with some firms using exclusive dealing arrangements and others contracting the sales function to independent agents who have ownership rights in the client list and who can represent a number of competing insurers. Independent agency insurers controlled 52 percent of the total market in 1994, and 71.8 percent of the commercial lines market.(1) The organizational form literature in property-liability insurance has largely treated ownership and distribution system choice separately. However, some overlap exists between the theory and empirical predictions across the ownership form and distribution system literature. For example, Mayers and Smith (1988) argue that stock insurers should be associated with a more complex mix of business than mutual insurers while Cummins and Weiss (1992), Regan and Tennyson (1996), and Regan (1997) argue that independent agency insurers should be preferred to exclusive dealers when complexity is higher. It is difficult to separate these effects empirically. An exception to treating these elements of organizational form as independent is Kim, Mayers, and Smith (1996), who argue that stock ownership and independent agency distribution are strategic complements, because independent agency is an effective device for minimizing agency costs that arise between owners and policyholders in a stock firm. Therefore, stockholder-owned insurers should choose independent agency distribution rather than exclusive dealing arrangements to minimize agency costs. While the authors of this article agree that independent agency distribution and stock ownership forms are likely to be strategic complements, the reasoning differs from that of Kim, Mayers, and Smith. An alternate explanation for the observed correlation between stock ownership form and independent agency distribution is that each of these elements offers advantages in certain lines of business and underwriting environments. In particular, the authors test the hypothesis that both stock ownership and independent agency distribution are more suited to complex lines of business and underwriting environments characterized by more risk than other combinations of ownership form and distribution system. Thus, rather than stockholder-owned firms choosing independent agency distribution, firms might first choose a business strategy, and then jointly choose ownership form and distribution system. The theory that supports this hypothesis is reviewed below. Several tests of the hypothesis are then presented. The direct correlation between ownership form and distribution system across lines of business is first measured using independence tests. Then, the authors compare the allocation of aggregate underwriting capacity to risky and complex lines of business between stock and non-stock insurers, and between independent agency and exclusive dealing insurers. …

Revisiting Almost Second-Degree Stochastic Dominance

Leshno and Levy [Leshno M, Levy H (2002) Preferred by “all” and preferred by “most” decision makers: Almost stochastic dominance. Management Sci. 48(8):1074--1085] established almost stochastic dominance to reveal preferences for most rather than all decision makers with an increasing and concave utility function. In this paper, we first provide a counterexample to the main theorem of Leshno and Levy related to almost second-degree stochastic dominance. We then redefine this dominance condition and show that the newly defined almost second-degree stochastic dominance is the necessary and sufficient condition to rank distributions for all decision makers excluding the pathological concave preferences. We further extend our results to almost higher-degree stochastic dominance. This paper was accepted by Peter Wakker, decision analysis.

Precautionary Effort: A New Look

While the concept of precautionary saving is well documented, that of precautionary effort has received relatively limited attention. In this note, we set up a two period model in order to analyze the conditions under which the introduction (or deterioration) of an independent background risk increases effort.

Pension Funding Incorporating Downside Risks

Abstract This research extends Haberman and Sung’s [Insurance: Mathematics and Economics 15 (1994) 151] and Chang’s [Insurance: Mathematics and Economics 24 (1999) 187] works to study optimal funding strategies through the control mechanism. The paper further generalizes the previous research in three ways. First, downside risks, under-funding risk and over-contributing risk, are included additionally in the risk minimization criterion to obtain the optimal solutions. Second, we allow the weighting factors in the performance criterion to belong to a broader parametric family. Third, the rates of investment returns are assumed to follow the auto-regressive process. The above three generalization indeed include traditional model as special cases. Furthermore, an actual case is employed to investigate their financial impacts on funding and contribution due to our generalization. The results show that neglecting to recognize the under-funding risk and the over-contribution risk will lead to a significant difference in optimal funding schedule. The weighting factors and the returns of investment also play critical roles in obtaining the optimal strategy.

Generalized Almost Stochastic Dominance

Almost stochastic dominance allows small violations of stochastic dominance rules to avoid situations where most decision makers prefer one alternative to another but stochastic dominance cannot rank them. While the idea behind almost stochastic dominance is quite promising, it has not caught on in practice. Implementation issues and inconsistencies between integral conditions and their associated utility classes contribute to this situation. We develop generalized almost second-degree stochastic dominance and almost second-degree risk in terms of the appropriate utility classes and their corresponding integral conditions, and extend these concepts to higher degrees. We address implementation issues and show that generalized almost stochastic dominance inherits the appealing properties of stochastic dominance. Finally, we define convex generalized almost stochastic dominance to deal with risk-prone preferences. Generalized almost stochastic dominance could be useful in decision analysis, empirical research (e.g., in finance), and theoretical analyses of applied situations.

Willingness to pay and the demand for lotto

Why do many bettors participate in an unfair gamble, in particular a lotto game, while at the same time purchase insurance? The willingness-to-pay for lotto is analysed to find a ‘rational’ explanation for a (local) risk-averters participation in an unfair bet. A reasonable case is found where bettors’ preference can be approximately characterized as a locally risk-averse and sufficiently prudent cubic function. Such bettors dislike risk but prefer standard third moment of the payoff. The result suggests that the traditional effective price for lotto demand may omit important explanatory variables. We thus propose an alternative method to examine the demand for lotto by incorporating the second and the third moments of lottos payoff. Evidence from Taiwan Lotto data supports that lotto bettors could be both (locally) risk-averse and rational.

Hedging Longevity Risk When Interest Rates are Uncertain

Abstract This paper proposes an asset liability management strategy to hedge the aggregate risk of annuity providers under the assumption that both the interest rate and mortality rate are stochastic. We assume that annuity providers can invest in longevity bonds, long-term coupon bonds, and shortterm zero-coupon bonds to immunize themselves from the risks of the annuity for the equity holders subject to a required profit. We demonstrate that the optimal allocation strategy can lead to the lowest risk under different yield curves and mortality rate assumptions. The longevity bond can also be regarded as an effective hedging vehicle that significantly reduces the aggregate risk of the annuity providers.

HIDDEN REGRET IN INSURANCE MARKETS

We examine insurance markets with two‐dimensional asymmetric information on risk type and on preferences related to regret. In contrast to Rothschild and Stiglitz ([Rothschild, M., 1976]), the equilibrium can be efficient; that is, it can coincide with the equilibrium under full information. Furthermore, we show that pooling, semipooling, and separating equilibria can exist. Specifically, there exist separating equilibria that predict a positive correlation between the level of insurance coverage and risk type, as in the standard economic models of adverse selection, but there also exist separating equilibria that predict a negative correlation between the level of insurance coverage and risk type. Since optimal choice of regretful customers depends on foregone alternatives, the equilibrium includes a contract that is offered but not purchased.

INCREASE IN RISK AND WEAKER MARGINAL-PAYOFF- WEIGHTED RISK DOMINANCE

This study investigates the comparative statics of an increase in risk for all risk-averse individuals with positive prudence. By extending the concept of risk dominance defined by Gollier (1995), this study provides the necessary and sufficient conditions-termed the weaker marginal-payoffweighted risk dominance-of unambiguous comparative statics for all riskaverse individuals with positive prudence. The article further applies the concept of weaker marginal-payoff-weighted risk dominance to examine the relationship between an increase in risk and the demand for proportional insurance and to demonstrate the difference between Golliers condition of risk dominance and weaker marginal-payoff-weighted risk dominance.

Optimal Tax Deductions for Net Losses under Private Insurance with an Upper Limit

Kaplow (1992b) shows that governments should not provide a tax deduction for net losses when a private insurance contract is available. However, his findings rest on the assumption that the private insurance is proportional coverage. We find that Kaplows conclusions may not hold when the private insurance contract contains an upper limit. The findings of our article show that Kaplows conclusions are sensitive to the assumption that the insurance contract is available in the private market.