Rachel J. Huang

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.

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.

Can Vehicle Maintenance Records Predict Automobile Accidents

This article proposes that vehicle maintenance records can provide useful information for predicting the probability that an owner will have an automobile accident. To test the hypothesis, we use a unique data set that is merged from an insurance company and a vehicle manufacturer in Taiwan. We find weak evidence to support our hypothesis. Among all the proxies for proper maintenance, we indicate that proper maintenance defined by the recommended kilometers is significantly negatively correlated with the loss probability in compulsory automobile liability insurance. The average loss probability decreases by 0.23 percent when the insured vehicle is properly maintained according to the recommended number of kilometers in the previous years, whereas the average loss probability for the overall sample is 0.49 percent. We further find that proper maintenance is insignificantly correlated with loss severity.

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.

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.

The Optimal Insurance Contract with Tax Deductions

We examine the impact of tax deductions on optimal insurance contracts. We find that, under a proportional tax deduction system, a nonzero deductible is obtained even though there are no variable costs for the insurer. On the other hand, the optimal coinsurance rate would remain at unity, even under the tax deduction system, when the insurer is risk neutral. A policy with an upper limit cannot be the optimal contract, no matter what tax deductions are provided for losses. Furthermore, unlike Kaplow’s (1992) finding that tax deductions reduce an individual’s demand for coinsurance, our results show that the implementation of tax deductions increases the deductible but may or may not decrease the coinsurance.

Measuring discrimination using principles of stochastic dominance

This note develops a new approach to measuring discrimination. A partial ordering of discrimination patterns is proposed that is consistent with the properties of second-degree stochastic dominance (SSD), which are related to changes in the distributions of either the reference (advantaged) or comparison (disadvantaged) group, while keeping the other groups distribution unchanged. Furthermore, a corresponding summary index is derived. This index provides a complete ordering to rank discrimination patterns and also satisfies the principles of SSD.