Addressing insurance price discrimination in an era of diversity,equity, and inclusion

The early 2020s diversity, equity, and inclusion movement has prompted debate about banning the use of suspect insurance pricing variables because they discriminate against protected classes, such as gender. This paper demonstrates how banning an insurance pricing variable currently used in insurance pricing models can result in regulatory adverse selection if the ban heterogeneously combines policyowners with different expected losses into the same risk class, contrary to risk-based pricing. The paper begins by describing several recent regulatory and judicial decisions to ban insurance pricing variables. It next describes the process used by insurers to set insurance prices, followed by a discussion of applicable insurance discrimination laws. Using a simple risk aversion model, the paper next examines whether a ban on gender-based auto insurance pricing in California in 2019 results in regulatory adverse selection. The paper concludes by describing possible alternative pricing variables available to auto insurers if gender-based pricing is banned.     

Constructing Asset Pricing Models With Specific Factor Loadings

We demonstrate how one can build pricing formulae in which factors other than beta may be viewed as determinants of asset returns. This is important conceptually as it demonstrates how the additional factors can compensate for a market portfolio proxy that is mis‐specified, and also shows how such a pricing model can be specified ex ante. The procedure is implemented by first selecting an ‘orthogonal’ portfolio which falls on the mean‐variance efficient frontier computed from the empirical average returns, variances and covariances on the equity securities of a large sample of firms. One then determines the inefficient index portfolio which leads to a vector of betas that when multiplied by the average return on the orthogonal portfolio, and which when subtracted from the vector of average returns for the firms comprising the sample, yields an error vector that is equal to the vector of numerical values for the variables that are to form the basis of the asset pricing formula. There will then be a perfect linear relationship between the vector of average returns for the firms comprising the sample, the vector of betas based on the inefficient index portfolio and such other factors that are deemed to be important in the asset pricing process. We illustrate computational procedures using a numerical example based on the quality of information contained in published corporate financial statements.     

Analysis of Participating Life Insurance Contracts: A Unification Approach

Fair pricing of embedded options in life insurance contracts is usually conducted by using risk‐neutral valuation. This pricing framework assumes a perfect hedging strategy, which insurance companies can hardly pursue in practice. In this article, we extend the risk‐neutral valuation concept with a risk measurement approach. We accomplish this by first calibrating contract parameters that lead to the same market value using risk‐neutral valuation. We then measure the resulting risk assuming that insurers do not follow perfect hedging strategies. As the relevant risk measure, we use lower partial moments, comparing shortfall probability, expected shortfall, and downside variance. We show that even when contracts have the same market value, the insurance company's risk can vary widely, a finding that allows us to identify key risk drivers for participating life insurance contracts.     

Capital Allocation for Insurance Companies—What Good IS IT?

In their 2001 Journal of Risk and Insurance article, Stewart C. Myers and James A. Read Jr. propose to use a specific capital allocation method for pricing insurance contracts. We show that in their model framework no capital allocation to lines of business is needed for pricing insurance contracts. In the case of having to cover frictional costs, the suggested allocation method may even lead to inappropriate insurance prices. Beside the purpose of pricing insurance contracts, capital allocation methods proposed in the literature and used in insurance practice are typically intended to help derive capital budgeting decisions in insurance companies, such as expanding or contracting lines of business. We also show that net present value analyses provide better capital budgeting decisions than capital allocation in general.     

Applications of Fuzzy Regression in Actuarial Analysis

In this article, we propose several applications of fuzzy regression techniques for actuarial problems. Our main analysis is motivated, on the one hand, by the fact that several articles in the financial and actuarial literature suggest using fuzzy numbers to model interest rate uncertainty but do not explain how to quantify these rates with fuzzy numbers. Likewise, actuarial literature has recently focused some of its attention in analyzing the Term Structure of Interest Rates (TSIR) because this is a key instrument for pricing insurance contracts. With these two ideas in mind, we show that fuzzy regression is suitable for adjusting the TSIR and discuss how to apply a fuzzy TSIR when pricing life insurance contracts and property‐liability policies. Finally, we reflect on other actuarial applications of fuzzy regression and develop with this technique the London Chain Ladder Method for obtaining Incurred But Not Reported Reserves.     

An empirical investigation of the welfare effects of banning wholesale price discrimination

Economic theory does not provide sharp predictions on the welfare effects of banning wholesale price discrimination: if downstream cost differences exist, then discrimination shifts production inefficiently, toward high‐cost retailers, so a ban increases welfare; if differences in price elasticity of demand across retailers exist, discrimination may increase welfare if quantity sold increases, so a ban reduces welfare. Using retail prices and quantities of coffee brands sold by German retailers, I estimate a model of demand and supply and separate cost and demand differences. Simulating a ban on wholesale price discrimination has positive welfare effects in this market, and less if downstream cost differences shrink, or with less competition.     

Cream Skimming: Innovations in Insurance Risk Classification and Adverse Selection

We demonstrate how innovations in insurance risk classification can lead to adverse selection, or cream skimming, against insurers that are slow to adopt such pricing innovations. Using a model in which insurers with insufficient pricing data cannot differentiate between low‐ and high‐risk policyholders and therefore charge both the same premium, we show how innovative insurers develop new risk classification data to identify overcharged low‐risk policyholders and attract them from rival insurers with reduced prices. Less innovative insurers thus insure a growing percentage of high‐risk customers, resulting in adverse selection attributable to their informational disadvantage. Next, we examine two cases in which “Big Data” innovations in risk classification led to concerns about cream skimming among U.S. auto insurers. First, we track the rapid adoption of credit‐based insurance scores as pricing variables in personal auto insurance markets. Second, we examine the growing popularity of usage‐based insurance programs like telematics, plans in which insurers use data on policyholders’ actual driving behavior to set prices that attract low‐risk customers. Issues associated with the execution of such pricing strategies are discussed. In both cases, we document how rival insurers quickly adopt successful innovations to reduce their exposure to adverse selection.     

Adverse Selection in Term Life Insurance Purchasing due to the BRCA1/2 Genetic Test and Elastic Demand

Consumer groups fear that the use of genetic testing information in insurance underwriting might lead to the creation of an underclass of individuals who cannot obtain insurance; thus, these groups want to ban insurance companies from accessing genetic test results. Insurers contend that such a ban might lead to adverse selection that could threaten their financial solvency. To investigate the potential effect of adverse selection in a term life insurance market, a discrete‐time, discrete‐state, Markov chain is used to track the evolution of twelve closed cohorts of women, differentiated by family history of breast and ovarian cancer and age at issue of a 20‐year annually renewable term life insurance policy. The insurance demand behavior of these women is tracked, incorporating elastic demand for insurance. During the 20‐year period, women may get tested for BRCA1/2 mutations. Each year, the insurer calculates the expected premiums and expected future benefit payouts which determine the following year's premium schedule. At the end of each policy year, women can change their life insurance benefit, influenced by their testing status and premium changes. Adverse selection could result from (i) differentiated benefits following test results; (ii) differentiated lapse rates according to test results; and (iii) differentiated reactions to price increases. It is concluded that with realistic estimates of behavioral parameters, adverse selection could be a manageable problem for insurers.     

Competitive cross‐subsidization

Cross‐subsidization arises naturally when firms with different comparative advantages compete for consumers with heterogeneous shopping patterns. Firms then face a form of co‐opetition, as they offer substitutes for one‐stop shoppers and complements for multi‐stop shoppers. When intense competition for one‐stop shoppers drives total prices down to cost, firms subsidize weak products with the profits made on strong products. Moreover, firms have incentives to seek comparative advantages on different products. Finally, banning below‐cost pricing increases firms' profits at the expense of one‐stop shoppers, which calls for a cautious use of below‐cost pricing regulations in competitive markets.     

Hidden insurance in a moral‐hazard economy

We analyze the general equilibrium of an economy in which a competitive industry produces nonexclusive insurance services. The equilibrium is inefficient because insurance contracts cannot control moral hazard, and welfare can be improved by policies that reduce insurance by increasing its price above marginal cost. We discuss how insurance production costs that exceed expected claim payments interact with moral hazard in determining the equilibrium's inefficiency, and show that these costs can make insurance premia so actuarially unfair as to validate the standard first‐order conditions we exploit in our analysis.     

Welfare Effects of Banning Genetic Information in the Life Insurance Market: The Case of BRCA1/2 Genes

We investigate whether regulations that ban insurance companies from access to individuals' genetic tests are likely to lead to substantial adverse selection costs for the specific example of the so‐called breast cancer (BRCA1/2) genes. Using a data set including economic, demographic, and relevant family background information to simulate the market for 10‐year term life insurance, we find generally only modest adverse selection costs associated with such a regulatory ban. However, for family background groups that are at high risk for carrying one of these genes, the efficiency cost of adverse selection may be significant should the test become widely adopted.     

Vertical integration,foreclosure, and productive efficiency

We analyze the consequences of vertical integration by a monopoly producer dealing with two retailers (downstream firms) of varying efficiency via secret two‐part tariffs. When integrated with the inefficient retailer, the monopoly producer does not foreclose the rival retailer due to an output‐shifting effect. This effect can induce the integrated firm to engage in below‐cost pricing at the wholesale level, thereby rendering integration procompetitive. Output shifting arises with homogeneous and differentiated products. Moreover, we show that integration with an inefficient retailer emerges in a model with uncertainty over retailers' costs, and this merger can be procompetitive in expectation.     

Dynamic limit pricing

I study a multiperiod model of limit pricing under one‐sided incomplete information. I characterize pooling and separating equilibria and their existence and determine when these involve limit pricing. For some parameter constellations, the unique equilibrium surviving a D1 type refinement involves immediate separation on monopoly prices. For others, there are limit price equilibria surviving the refinement in which different types may initially pool and then (possibly) separate. Separation involves setting prices such that the inefficient incumbent's profits from mimicking are negative. As the horizon increases or as firms become more patient, limit pricing becomes increasingly difficult to sustain in equilibrium.     

Information congestion

Unsolicited advertising messages vie for scarce attention. “Junk” mail, “spam” e‐mail, and telemarketing calls need both parties to exert effort to generate transactions. Message receivers supply attention according to average message benefit, while the marginal sender determines congestion. Costlier transmission may improve average message benefit so more messages are examined. Too many (too few) messages may be sent, or the wrong ones. A Do‐Not‐Call policy beats a ban, but too many individuals opt out. A monopoly gatekeeper performs better than personal access pricing if nuisance costs to receivers are moderate. The welfare results still hold when messages are presorted (triage).     

Liability insurance under the negligence rule

We incorporate the concept of evidentiary standard to the analysis of the negligence rule under liability insurance and court errors. When the postaccident evidence is privately contractible and not too noisy, efficiency is achieved by both strict liability and a negligence rule with appropriate due care and evidentiary standards. When the evidence is not directly contractible, trial outcomes represent useful contractible information for the risk‐incentives tradeoff in the liability insurance policy. Strict liability is then inefficient and dominated by the negligence rule. The negligence rule can itself be improved upon by decoupling damages from the harm suffered by the victim.     

A revised option pricing formula with the underlying being banned from short selling

An important issue in derivative pricing that hasn't been explored much until very recently is the impact of short selling to the price of an option. This paper extends a recent publication in this area to the case in which a ban of short selling of the underlying alone is somewhat less ‘effective’ than the extreme case discussed by Guo and Zhu [Equal risk pricing under convex trading constraints. J. Econ. Dyn. Control, 2017, 76, 136–151]. The case presented here is closer to reality, in which the effect of a ban on the underlying of an option alone may quite often be ‘diluted’ due to market interactions of the underlying asset with other correlated assets. Under a new assumption that there exists at least a correlated asset in the market, which is allowed to be short sold and thus can be used by traders for hedging purposes even though short selling of the underlying itself is banned, a new closed-form equal-risk pricing formula for European options is successfully derived. The new formula contains two distinguishable advantages; (a) it does not induce any significantly extra burden in terms of numerically computing option values, compared with the effort involved in using the Black–Scholes formula, which is still popularly used in finance industry today; (b) it remains simple and elegant as only one additional parameter beyond the Black–Scholes formula is introduced, to reflect the dilution effect to the ban as a result of market interactions.     

Fair Valuation of a Guaranteed Life Insurance Participating Contract Embedding a Surrender Option

In this article we deal with the problem of pricing a guaranteed life insurance participating policy, sold in the Italian market, which embeds a surrender option. This feature is an American‐style put option that enables the policyholder to sell back the contract to the insurer at the cash surrender value. Employing a recursive binomial formula patterned after the Cox, Ross, and Rubinstein (1979) discrete option pricing model we compute, first of all, the total price of the contract, which also includes a compensation for the participation feature (“participation option,” henceforth). Then this price is split into the value of three components: the basic contract, the participation option, and the surrender option. The numerical implementation of the model allows us to catch some comparative statics properties and to tackle the problem of suitably fixing the contractual parameters in order to obtain the premium computed by insurance companies according to standard actuarial practice.     

Timing of Sale,Pricing, and Cost Information: Evidence from the Airline Industry*

This study examines the association between when an airline sells its passenger seats and the pricing method (marginal cost or full cost) it employs. Prior literature suggests that when firms are able to change prices during the selling period, the optimality of full cost pricing or marginal cost pricing depends on when demand information is revealed during the period between capacity commitment decisions and time of sale. Full cost‐based pricing is appropriate in determining capacity commitment and prices simultaneously, while marginal cost provides more relevant information for pricing when capacity has been committed. Using the price and cost data from a sample of four U.S. domestic airlines, we find that full cost explains price variations of first‐day sales robustly. The adjusted R² of the marginal cost pricing model is larger in the sample of sales two days prior to departure than in the sample of first‐day sales. In the analysis of the sample of sales two days prior to departure, we find that, based on the adjusted R² of the full cost pricing and marginal cost pricing models, the explanatory power of marginal cost pricing is relatively weaker than full cost pricing. Our results document the use of different cost information along the dynamic change of price and provide implications in understanding the role of cost information in setting prices.     

Pricing Double-Trigger Reinsurance Contracts: Financial Versus Actuarial Approach

This article discusses various approaches to pricing double‐trigger reinsurance contracts—a new type of contract that has emerged in the area of ‘‘alternative risk transfer.’’ The potential coverage from this type of contract depends on both underwriting and financial risk. We determine the reinsurer's reservation price if it wants to retain the firm's same safety level after signing the contract, in which case the contract typically must be backed by large amounts of equity capital (if equity capital is the risk management measure to be taken). We contrast the financial insurance pricing models with an actuarial pricing model that has as its objective no lessening of the reinsurance company's expected profits and no worsening of its safety level. We show that actuarial pricing can lead the reinsurer into a trap that results in the failure to close reinsurance contracts that would have a positive net present value because typical actuarial pricing dictates the type of risk management measure that must be taken, namely, the insertion of additional capital. Additionally, this type of pricing structure forces the reinsurance buyer to provide this safety capital as a debtholder. Finally, we discuss conditions leading to a market for double‐trigger reinsurance contracts.