Strategic Demand for Insurance

We focus on the corporate demand for insurance under duopoly. We consider the case in which firms purchase insurance in order to enhance their competitiveness. We show that a higher level of corporate insurance makes a firm more aggressive and its competitor less aggressive in the output market (strategic effect). The optimal coverage of insurance is determined by comparing the strategic effect of insurance and the cost of insurance. The optimal coverage is positive if the strategic effect is greater than the cost of insurance. An interesting implication is that a risk‐neutral firm may purchase actuarially unfair insurance. The main strategic effect of insurance comes from the fact that firms purchase insurance before they produce outputs. Insurance makes firms more aggressive due to the limited risk costs of firms.     

The Demand for Insurance With an Upper Limit on Coverage

The demand for insurance is examined when the indemnity schedule is subject to an upper limit. The optimal contract is shown to display full insurance above a deductible up to the cap. Some results derived in the standard model with no upper limit on coverage turn out to be invalid; the optimal deductible of an actuarially fair policy is positive and insurance may be a normal good under decreasing absolute risk aversion. An increase in the upper limit would induce the policyholder with constant absolute risk aversion to reduce his or her optimal deductible and therefore this would increase the demand for insurance against small losses.     

The Impact of Insurance Prices on Decision Making Biases: An Experimental Analysis

This article tests whether the use of endogenous risk categorization by insurers enables consumers to make better‐informed decisions even if they do not choose to purchase insurance. We do so by adding a simple insurance market to an experimental test of optimal (Bayesian) updating. In some sessions, no insurance is offered. In others, actuarially fair insurance prices are posted, and a subset of subjects is allowed to purchase this insurance. We find significant differences in the decision rules used depending on whether one observes insurance prices. Although the majority of choices correspond to Bayesian updating, the incidence of optimal decisions is higher in sessions with an insurance option. Most subjects given the option to purchase actuarially fair insurance choose to do so. However, fewer subjects purchase insurance when the probability of a loss is higher.     

Corporate capital structure and pension-funding strategy

This article provides an integrated analysis of pension funding and corporate financing strategies in the presence of default risk. The article shows that when the marginal personal income tax rate is constant, the financing decision with respect to pension funding is influenced entirely by tax considerations. When the marginal personal income tax is progressive, the optimal financing of pension funding depends on the cyclical nature of the firm (as characterized by the sign of beta), the riskiness of pension assets, and ERISA regulations concerning the pension-benefit guaranty rate, the marginal pension insurance premium and the firm's legal responsibility for its unfunded pension obligations. It is shown that a necessary condition for partial pension funding is that the marginal insurance premium imposed by PBGC must be less than actuarially fair, and a necessary condition for pension funding to be financed by both debt and equity is that beta must be positive.     

Insurance Markets With Differential Information

This article attempts to understand the outcomes when each party of an insurance contract simultaneously has superior information. I assume that policyholders have superior information about specific risks while insurers have superior information about general risks. I find that low-general-risk policyholders purchase insurance, while high-general-risk policyholders are self-insured. Among the low-general-risk policyholders, high-specific-risk policyholders purchase full insurance, while low-specific-risk policyholders purchase partial insurance. When insurers can strategically publicize their information, efficiency is improved because high-general-risk policyholders purchase actuarially fair insurance. The market segmentation is also found based on the general-risk type and the publicizing of information.     

Consumers’ collision insurance decisions: a mental models approach to theory evaluation

Using interviews with 74 drivers, we elicit and analyze how people think about collision insurance coverage and decide whether to buy coverage, and if so, what deductible level to carry. We compare respondents’ judgments and behaviors to predictions of three models: baseline expected utility (EU) theory, which predicts that insurance is an inferior good, meaning more wealthy people buy less; a modified EU model, which incorporates income constraints and suggests that property insurance is a normal good, meaning more wealthy people buy more; and a mental accounting model which predicts that consumers budget income across consumption categories. The results suggest they purchase insurance as a normal good, guided by a cognitive model that emphasizes budget constraints. Verbal reports reveal a desire to balance two conflicting goals in deductible decisions: keeping premiums ‘affordable’ and keeping deductible level ‘affordable.’ Thus, wealth does not distinguish people by risk aversion, but by ability to pay. In other words, the behavior of less wealthy people is not driven by greater risk aversion, but by their lesser ability to pay, both now and later. We find that a simple heuristic using only vehicle value accounts for most decisions of whether to purchase optional collision coverage: out of 45 respondents who did not have loans on their vehicles, 90% of those with vehicles worth more than $1000 carried collision coverage, while less than 30% of those with lower‐valued vehicles did.     

The design of an optimal insurance contract for irreplaceable commodities

This paper discusses optimal insurance contract for irreplaceable commodities. To describe the dual impacts on individuals when a loss occurs to the insured irreplaceable commodities, we use a state-dependent and bivariate utility function, which includes both the monetary wealth and sentimental value as two arguments. We show that over (full, partial) insurance is optimal when a decrease in sentimental value will increase (not change, decrease, respectively) the marginal utility of monetary wealth. Moreover, a non-zero deductible exists even without administration costs. Furthermore, we demonstrate that a positive fixed reimbursement is optimal if (1) the premium is actuarially fair, (2) the monetary loss is a constant, and (3) the utility function is additively separable and the marginal utility of money is higher in the loss state than in the no-loss state. We also characterize comparative statics of fixed-reimbursement insurance under an additively separable preference assumption. JEL Classification G22 · D86 The author acknowledge funding from National Science Council in Taiwan (NSC93-2416-H-130-020).     

Do Mandatory Hedge Disclosures Discourage or Encourage Excessive Speculation?

In order to shed some light on the desirability of hedge disclosures, I investigate the consequences of hedge disclosures on a firm's risk management strategy. Several major results emerge from this analysis. First, greater transparency about a firm's derivative activities is not necessarily a panacea for imprudent risk management strategies. I show that such transparency actually induces the firm to take excessive speculative positions in the derivative market. Second, I show that the firm may choose a prudent risk management strategy in the absence of hedge disclosures. However, the selection of a prudent risk management comes at a cost. The firm's production policy is distorted in the absence of hedge disclosures.
These findings suggest that regulators must carefully investigate the trade-offs between production distortions and risk management distortions in evaluating the desirability of mandatory hedge disclosures for all firms.     

Deposit insurance, bank regulation, and financial system risks

Empirical evidence is presented to show that in modern times banks can hedge liquidity shocks but could not do so prior to FDIC insurance. However, the government's limitations in properly pricing FDIC insurance are leading to many current examples of moral hazard. A model is presented to show that if insurance premiums are set to be “actuarially fair,” incentives for banks to take excessive systematic risks remain. Motivated by empirical evidence that money market mutual funds also can hedge liquidity shocks, I consider an alternative government insurance system that mitigates distortions to risk-taking yet preserves liquidity hedging and information synergies.     

RISK-TAKING INCENTIVES OF BANKS AND RISK-ADJUSTED DEPOSIT INSURANCE

The manager of a depository institution is shown to exhibit risk-taking behavior under the current insurance arrangement. Perfect monitoring or risk-based deposit insurance would eliminate this incentive if information were symmetric between bank managers and the insuring agency. Absent symmetric information, it is shown that a recently suggested scheme, where insurers collect insurance premiums based on projected and actual risk levels, does not control the risk-taking incentive. The only way to control this incentive through insurance rates is to levy a relatively high premium, which is not actuarially fair.     

On the Possibility of a Private Crop Insurance Market: A Spatial Statistics Approach

Risk theory tells us if an insurer can effectively pool a large number of individuals to reduce total risk, the insurer can then provide insurance by charging a premium close to the actuarially fair rate. However, a common belief exists that risk can be effectively pooled only when random loss is independent. Therefore crop insurance markets cannot survive without government subsidy because crop yields are not independent among growers. In this article, we take a spatial statistics approach to examine the effectiveness of risk pooling for crop insurance under correlation. We develop a method for evaluating the effectiveness of risk pooling under correlation and apply the method to three major crops in the United States: wheat, soybeans, and corn. The empirical study shows that yields for the three crops present zero or negative correlation when two counties are far apart, which complies with a weaker condition than independence, finite‐range positive dependency. The results show that effective risk pooling is possible and reveal a high possibility of a private crop insurance market in the United States.     

A note on Mossin’s theorem for deductible insurance given random initial wealth

Mossin’s theorem for deductible insurance given random initial wealth is re-examined. For a fair premium, it is shown that a necessary and sufficient condition, in the spirit of the Generalized Mossin Theorem for coinsurance, is impossible using the notion of expectation dependence. Next, it is established that for a fair premium, full insurance will be optimal for a risk-averse individual if the random loss and the random initial wealth are negative quadrant dependent, improving upon an extant result in the literature. In view of a set of examples given in this paper, such a sufficient condition cannot be obtained using the notion of expectation dependence. Finally, for an unfair premium, it is shown that partial insurance will always be optimal, irrespective of the risk preference of the individual as well as the dependence structure between the random loss and the random initial wealth.     

The Liquidity Demand for Corporate Property Insurance

This article suggests that liquidity may be an important reason for a corporation to purchase property insurance. A model of a risk‐neutral producer facing an endogenously determined risk of property damage under an output contract that penalizes underproduction is formulated to exemplify such a real need of liquidity. Under the output contract, the producer may purchase full unfavorable property insurance even when postloss financing is available. Surprisingly, the conclusion may still hold when the cost of postloss financing equals that of long‐term capital, provided that the rate of underproduction penalty is sufficiently high. Similar conclusions apply when postloss financing is replaced by planned internal reserve (self‐insurance) that may be invested in the short run at an interest rate that is lower than the long‐term cost of capital. When the capital market is perfect, however, the holding of planned internal reserve eliminates the purchase of actuarially unfavorable property insurance.     

Financing and the demand for corporate insurance

In this paper we examine the insurance decision of a firm with private information regarding its cash flows and insurable losses. We show that, even in the absence of bankruptcy costs and information production by insurers, the firm's attempts to hedge its information risk can induce it to demand insurance. If higher operating revenues are accompanied by a lower insurance risk, the firm will choose to self-insure. In contrast, if higher operating revenues are accompanied by a higher insurance risk, the firm will demand insurance. In fact, if its insurable losses are relatively small, the firm will fully insure its losses. Further, if there exists considerable uncertainty regarding the firm's insurance risk, the level of coverage demanded by the firm is dependent on its private information, with higher levels of coverage signaling favorable information regarding the firm's future operations.     

Guaranteed renewable life insurance under demand uncertainty

Guaranteed renewability (GR) is a prominent feature in many health and life insurance markets. We develop a model that includes unpredictable (and unobservable) fluctuations in demand for life insurance as well as changes in risk type (observable) over individuals' lifetimes. The presence of demand type heterogeneity leads to the possibility that optimal GR contracts may have a renewal price that is either above or below the actuarially fair price of the lowest risk type in the population. Individuals whose type turns out to be high risk but low demand renew more of their GR insurance than is efficient due to the attractive renewal price. This results in imperfect insurance against reclassification risk. Although a first‐best efficient contract is not possible in the presence of demand type heterogeneity, the presence of GR contracts nonetheless improves welfare relative to an environment with only spot markets.     

Insurance and Endogenous Bankruptcy Risk: When is it Rational to Choose Gambling,Insurance, and Potential Bankruptcy?

We examine the coexistence of insurance and gambling in the context of limited liability. We develop a model where actuarially fair insurance is available to a risk-averse decision maker for a liability risk with non-bankrupting severity. The remaining wealth may be invested in a zero expected value risky project (i.e., gambled). The risk of bankruptcy is endogenous since either fully insuring or forgoing the project will guarantee solvency. We show that, for a range of parameters, it is optimal to both insure and gamble. The amounts insured and invested are chosen to create the potential for bankruptcy. Our results are robust to the cases where the risky project can cause bankruptcy without a liability loss and where the risky project’s expected return is nonzero.     

Optimal insurance contract and coverage levels under loss aversion utility preference

This study develops an optimal insurance contract endogenously and determines the optimal coverage levels with respect to deductible insurance, upper-limit insurance, and proportional coinsurance, and, by assuming that the insured has an S-shaped loss aversion utility, the insured would retain the enormous losses entirely. The representative optimal insurance form is the truncated deductible insurance, where the insured retains all losses once losses exceed a critical level and adopts a particular deductible otherwise. Additionally, the effects of the optimal coverage levels are also examined with respect to benchmark wealth and loss aversion coefficient. Moreover, the efficiencies among various insurances are compared via numerical analysis by assuming that the loss obeys a uniform or log-normal distribution. In addition to optimal insurance, deductible insurance is the most efficient if the benchmark wealth is small and upper-limit insurance if large. In the case of a uniform distribution that has an upper bound, deductible insurance and optimal insurance coincide if benchmark wealth is small. Conversely, deductible insurance is never optimal for an unbounded loss such as a log-normal distribution.     

The pricing of deposit insurance in the presence of systematic risk

Based on the Merton (1977) put option framework, we develop a deposit insurance pricing model that incorporates asset correlations, a measurement for the systematic risk of a bank, to account for the risk of joint bank failures. Estimates from our model suggest that actuarially fair risk-based deposit insurance that considers only individual bank failure risk is underpriced, leaving insurance providers exposed to net losses. Our estimates also capture the size premium where big banks are priced with higher deposit insurance than small banks. This result is particularly relevant to the current regulatory concerns on big banks that are too-big-to-fail. Above all, our approach provides a unifying framework for integrating risk-based deposit insurance with risk-based Basel capital requirements.     

Risk classification with on-demand insurance

On-demand insurance is an innovative business model from the InsurTech space, which provides coverage for episodic risks. It makes use of a simple fact in a practical way: People differ in their frequency of exposure as well as the probability of loss. The extra dimension of heterogeneity can be used to screen the insured and shifts the utility-possibility frontier outward. We provide a sufficient condition under which type-specific full insurance at the actuarially fair price is incentive compatible. We also show that our results hold for various real-world implementations of on-demand insurance.     

The Effect of Pre-commitment and Past-Experience on Insurance Choices: An Experimental Study

This paper reports results from an experimental study that investigates insurance behaviors in low-probability, high-loss risk situations. The study reveals that insurance behaviors may depend on the length of the commitment period of insurance policies, namely the period during which individuals commit themselves to maintain the same insurance decision. The results of this study also seem to support the predictions of the Dual Theory concerning the demand for co-insurance policies, that is to say the preference of individuals for extreme (null or full) levels of insurance coverage. This study also suggests that prior risk occurrences influence subsequent insurance choices. The paper provides a new possible explanation about the puzzling fact that people usually fail to obtain insurance against disaster-type risks such as natural disasters, even when premiums are close to actuarially fair levels.