The Impact of Disability Insurance on a Portfolio of Life Insurances

The aim of this article is to study the impact of disability insurance on an insurer's risk situation for a portfolio that also consists of annuity and term life contracts. We provide a model framework using discrete time nonhomogeneous bivariate Markov renewal processes and in a simulation study focus on diversification benefits as well as potential natural hedging effects (risk-minimizing or risk-immunizing portfolio compositions) that may arise within the portfolio because of the different types of biometric risks. Our analyses emphasize that disability insurances are a less efficient tool to hedge shocks to mortality and that their high sensitivity toward shocks to disability risks cannot be easily counterbalanced by other life insurance products. However, the addition of disability insurance can still considerably lower the overall company risk.     

On the Lack of Participating Policy Usage by Stock Insurance Companies

Stock insurers can reduce or eliminate agency conflicts between policyholders and stockholders by issuing participating insurance. Despite this benefit, most stock companies don't offer participating contracts. This study explains why. We study an equilibrium with both stock and mutual insurers in which stockholders set premiums to provide a fair expected return on their investment, and with a policyholder who chooses the insurance contract that maximizes her expected utility. We demonstrate that stockholders cannot profitably offer fully participating contracts, but can profitably offer partially participating insurance. However, when the policyholder participation fraction is high, the fair‐return premium is so large that the policyholder always prefers fully participating insurance from the mutual company. Policies with lower levels of policyholder participation are optimal for policyholders with relatively high risk aversion, though such policies are usually prohibited by insurance legislation. Thus, the reason stock insurers rarely issue participating contracts isn't because the potential benefits are small or unimportant. Rather, profitability or regulatory constraints simply prevent stock insurers from exercising those benefits in equilibrium.     

Do Portfolio Manager Contracts Contract Portfolio Management?

Most mutual fund managers have performance‐based contracts. Our theory predicts that mutual fund managers with asymmetric contracts and mid‐year performance close to their announced benchmark increase their portfolio risk in the second part of the year. As predicted by our theory, performance deviation from the benchmark decreases risk‐shifting only for managers with performance contracts. Deviation from the benchmark dominates incentives from the flow‐performance relation, suggesting that risk‐shifting is motivated more by management contracts than by a tournament to capture flows.     

Temporal Profitability and Pricing of Long-Term Care Insurance

Equilibrium models of dynamic insurance markets can be bifurcated according to underlying assumptions about whether or not insurers commit to long‐term contracts. The difference is substantial in that commitment models imply price highballing over time while no‐commitment models indicate price lowballing. Extant empirical studies provide mixed evidence, however. We use long‐term care (LTC) insurance data, which allow us both to better control for heterogeneous, observable risk, to examine dynamic profitability and pricing in a relatively young, innovative insurance market. Our tests generally indicate temporal price lowballing, thereby providing support for the no‐commitment models.     

Fair valuation of cliquet-style return guarantees in (homogeneous and) heterogeneous life insurance portfolios

Participating life insurance contracts allow the policyholder to participate in the annual return of a reference portfolio. Additionally, they are often equipped with an annual (cliquet-style) return guarantee. The current low interest rate environment has again refreshed the discussion on risk management and fair valuation of such embedded options. While this problem is typically discussed from the viewpoint of a single contract or a homogeneous* insurance portfolio, contracts are, in practice, managed within a heterogeneous insurance portfolio. Their valuation must then – unlike the case of asset portfolios – take account of portfolio effects: Their premiums are invested in the same reference portfolio; the contracts interact by a joint reserve, individual surrender options and joint default risk of the policy sponsor. Here, we discuss the impact of portfolio effects on the fair valuation of insurance contracts jointly managed in (homogeneous and) heterogeneous life insurance portfolios. First, in a rather general setting, including stochastic interest rates, we consider the case that otherwise homogeneous contracts interact due to the default risk of the policy sponsor. Second, and more importantly, we then also consider the case when policies are allowed to differ in further aspects like the guaranteed rate or time to maturity. We also provide an extensive numerical example for further analysis.     

On the Relative Performance of Investment‐Grade Corporate Bonds with Differing Maturities

We find that short‐maturity investment‐grade corporate bonds perform better, controlling for risk differences, than similar bonds with longer maturities. Our results are at least partially attributable to insurance companies’ trading behavior and align with the preferred‐habitat theory of the term structure. We find that insurance‐company purchases create a strong demand for long‐term bonds and that their rebalancing activity results in sales of short‐term bonds. As documented by extant literature, such demand‐supply imbalance is not easily resolved by arbitrageurs or firms seeking to time the market with bond issuance.     

Valuation portfolio in non-life insurance

The purpose of this paper is the construction of the Valuation Portfolio (VaPo) for a non-life insurance company. The VaPo represents the obligations of the insurer for the whole period of his insurance contracts. These obligations are not simply measured by a one-dimensional figure (as standard for reserves in practice), but are expressed as a portfolio of financial instruments. Hence, the actuarial reserves become multidimensional. The financial instruments in the VaPo are a properly chosen basis to represent the future cashflows resulting from the insurance contracts.

In this setup, financial and technical risks are clearly separated. The financial fluctuations derive from the basis elements, the technical fluctuations are covered by an increased number of basis elements (VaPo protected against technical risks). We show how this protection can be calculated in the case of a non-life insurance company.     

Health and Mortality Delta: Assessing the Welfare Cost of Household Insurance Choice

We develop a pair of risk measures, health and mortality delta, for the universe of life and health insurance products. A life‐cycle model of insurance choice simplifies to replicating the optimal health and mortality delta through a portfolio of insurance products. We estimate the model to explain the observed variation in health and mortality delta implied by the ownership of life insurance, annuities including private pensions, and long‐term care insurance in the Health and Retirement Study. For the median household aged 51 to 57, the lifetime welfare cost of market incompleteness and suboptimal choice is 3.2% of total wealth.     

Dynamic Insurance Contracts and Adverse Selection

We take a dynamic perspective on insurance markets under adverse selection and study a dynamic version of the Rothschild and Stiglitz model. We investigate the nature of dynamic insurance contracts by considering both conditional and unconditional dynamic contracts. An unconditional dynamic contract has insurance companies offering contracts where the terms of the contract depend on time, but not on the occurrence of past accidents. Conditional dynamic contracts make the actual contract also depend on individual past performance (such as in car insurances). We show that dynamic insurance contracts yield a welfare improvement only if they are conditional on past performance. With conditional contracts, the first‐best can be approximated if the contract lasts long. Moreover, this is true for any fraction of low‐risk agents in the population.     

Corporate Insurance as a Necessary Form of Consultant–Investigator Contract

Existing literature argues that corporate insurance is purchased because the insurance company produces risk management information for publicly held corporations. In this article, we address a fundamental question as to why other financial intermediaries cannot perform the same information production function as the insurance company. We argue that when the risk manager of the firm performs multiple tasks and needs consulting and investigation services from an outside agent for efficient risk management, the optimal contract with the agent has to be in the form of an insurance contract. Other types of contracts, such as flat-fee contracts, cannot be optimal. Therefore, the insurance company is ideally suited to provides these services.     

Predictable Investment Horizons and Wealth Transfers among Mutual Fund Shareholders

This study analyzes the distribution of investment horizons in a large, proprietary panel of all shareholders in one no‐load mutual fund family. A proportional hazards model shows that there are observable shareholder characteristics that enable the fund to predict reliably on the day each account is opened whether the account will be short term or long term. Simulations show that the liquidity costs imposed on the fund by the expected short‐term shareholders are significantly greater than those imposed by the expected long‐term shareholders. Combining these results, the analysis argues that mutual funds do not provide equitable liquidity‐risk insurance.     

On systematic mortality risk and risk-minimization with survivor swaps

A new market for so-called mortality derivatives is now appearing with survivor swaps (also called mortality swaps), longevity bonds and other specialized solutions. The development of these new financial instruments is triggered by the increased focus on the systematic mortality risk inherent in life insurance contracts, and their main focus is thus to allow the life insurance companies to hedge their systematic mortality risk. At the same time, this new class of financial contract is interesting from an investor's point of view, since it increases the possibility for an investor to diversify the investment portfolio. The systematic mortality risk stems from the uncertainty related to the future development of the mortality intensities. Mathematically, this uncertainty is described by modeling the underlying mortality intensities via stochastic processes. We consider two different portfolios of insured lives, where the underlying mortality intensities are correlated, and study the combined financial and mortality risk inherent in a portfolio of general life insurance contracts. In order to hedge this risk, we allow for investments in survivor swaps and derive risk-minimizing strategies in markets where such contracts are available. The strategies are evaluated numerically.     

Risk Mutualization and Competition in Insurance Markets

The aim of this paper is to analyze the impact of mutual firms on competition in the insurance market. We distinguish two actors in this market: mutual firms, which belong to their pooled members, and traditional companies, which belong to their shareholders. Our approach differs from the literature by one crucial assumption: the expected utility of the consumers depends on the size of their insurance firm, which generates network externalities in this market. Thus, the choice of a contract results in a trade-off between the premium level and the probability of that premium being ex-post adjusted. The optimal contract offered by a mutual firm involves a systematic ex-post adjustment (negative or positive), while the contracts a company offers imply a fixed premium that is possibly negatively adjusted at the end of the contractual period. In an oligopoly game, we show that three types of configurations are possible at equilibrium: either one mutual firm or insurance company is active, or a mixed structure emerges in which two or more companies share the market with or without a mutual firm.     

保险公司负债公允价值的评估

保险公司的资产与负债按照财务报告或风险管理的要求要用公允价值来表示其价值。保险公司负债主要由各种类型的保险合同组成。尽管金融产品的交易非常活跃,市场价格可以相对容易地获得,但像保险合同这样缺乏交易市场,并且风险是非系统化的金融产品的公允价值的计算却十分困难。通过分层次的方法可以有效地评估金融工具的公允价值,其中评估保险公司负债的公允价值最常用的方法是现值法。现值法中包含了直接法与间接法两种本质上等价的方法。本文对这两种方法分别作了分析,并提出了在评估保险公司负债的公允价值时需要考虑的一些现实问题。     

Arbitrage and Viability in Insurance Markets

Insurance markets are subject to transaction costs and constraints on portfolio holdings. Therefore, unlike the frictionless asset markets case, viability is not equivalent to absence of arbitrage possibilities. We use the concept of unbounded arbitrage to characterize viable prices on a complete and an incomplete insurance market. In the complete market, there is an insurance contract for every possible event. In the incomplete market, risk can be insured through proportional and excess of loss like insurance contracts. We show how the the structure of viable prices is affected by the portfolio constraints, the transaction costs, and the structure of marketed contracts.     

On the Demand for Portfolio Insurance

While insurers manage underwriting risk with various methods including reinsurance, insurers increasingly manage asset risk with options, futures, and other derivatives. Previous research shows that buyers of portfolio insurance pay considerably for downside protection. We add to this literature by providing the first evidence on the cost of portfolio insurance, the payoff to portfolio insurance, and the relative demand for portfolio insurance across VIX levels. We find that the demand for portfolio insurance is relatively high at low levels of VIX, suggesting purchasers demand more downside protection when this protection is cheap on an absolute basis (but expensive on a relative basis). We also provide the first evidence on the hedging behavior of specific investor classes and show that the demand for portfolio insurance is driven by retail investors (individuals) who buy costly insurance from institutional investors. Results are consistent with other types of paradoxical insurance‐buying behavior.     

Estimating portfolio risk for tail risk protection strategies

We forecast portfolio risk for managing dynamic tail risk protection strategies, based on extreme value theory, expectile regression, copula‐GARCH and dynamic generalized autoregressive score models. Utilizing a loss function that overcomes the lack of elicitability for expected shortfall, we propose a novel expected shortfall (and value‐at‐risk) forecast combination approach, which dominates simple and sophisticated standalone models as well as a simple average combination approach in modeling the tail of the portfolio return distribution. While the associated dynamic risk targeting or portfolio insurance strategies provide effective downside protection, the latter strategies suffer less from inferior risk forecasts, given the defensive portfolio insurance mechanics.     

Does the Failure of the Expectations Hypothesis Matter for Long‐Term Investors?

We solve the portfolio problem of a long‐run investor when the term structure is Gaussian and when the investor has access to nominal bonds and stock. We apply our method to a three‐factor model that captures the failure of the expectations hypothesis. We extend this model to account for time‐varying expected inflation, and estimate the model with both inflation and term structure data. The estimates imply that the bond portfolio of a long‐run investor looks very different from the portfolio of a mean‐variance optimizer. In particular, time‐varying term premia generate large hedging demands for long‐term bonds.     

Valuation of Equity-Linked Insurance and Annuity Products with Binomial Models

Abstract

In this paper we develop a valuation method for equity-linked insurance products. We assume that the premium information of term life insurances, pure endowment insurances, and endowment insurances at all maturities is obtainable within a company or from the insurance market. Using a method similar to that of Jarrow and Turnbull (1995), we derive three martingale probability measures associated with these basic insurance products. These measures are agedependent, include an adjustment for the mortality risk, and reproduce the premiums of the respective insurance products. We then extend the martingale measures to include the financial market information using copulas and use them to evaluate equity-linked insurance contracts and equity-indexed annuities in particular. This is different from the traditional approach under which diversification of mortality risk is assumed. A detailed numerical analysis is performed for various existing equity-indexed annuities in the North American market.     

Zur bedeutung einer Ausfallbedrohtheit von Versicherungskontrakten — ein Beitrag zur Behavioral Insurance

Kahneman / Tversky 1979 introduced the notion of so-called probabilistic insurance contracts. These are insurance policies involving a small probability that the consumer is not reimbursed because of a possible default of the insurance company. Extending the study ofWakker / Thaler / Tversky 1997, the present study contains an experimental analysis of the willingness of potential policyholders to pay for probabilistic insurance in dependency on the rating of the insurance company. It can be shown that people dislike probabilistic insurance and demand a substantial reduction in the premium to compensate for default risk. This reduction is rising with the default risk of the company. In addition, the results show a new phenomenon. The more an insurance company is threatened by default risk the less people are willing to accept contracts of this company at all. Finally the paper discusses implications for the control of insurance companies.