Relational contracts with subjective peer evaluations

We study optimal dynamic contracting for a firm with multiple workers where compensation is based on public performance signals and privately reported peer evaluations. We show that if evaluation and effort provision are done by different workers (e.g., consider supervisor‐agent hierarchy), first‐best can be achieved even in a static setting. However, if each worker both exerts effort and reports peer evaluations (e.g., consider team setting), effort incentives cannot be decoupled from truth‐telling incentives. This makes the optimal static contract inefficient. Relational contracts based on public signals increase efficiency. Interestingly, the optimal contract may ignore signals that are informative about effort.     

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.     

论投保人缴纳保费或保险公司签发保单附条件条款的法律效力

我国保险实践中普遍将投保人缴纳保费或者保险公司签发保单作为保险合同的成立、生效或者保险责任开始的条件。但该条件不是新《保险法》规定的附条件保险合同所指的条件。同时该附条件条款赋予了保险公司对要约进行承诺时或者履行合同义务时不受时间限制的权利,该附条件条款因不具有合理性应为无效合同条款。     

Hedging with Two Futures Contracts: Simplicity Pays

We propose to use two futures contracts in hedging an agricultural commodity commitment to solve either the standard delta hedge or the roll‐over issue. Most current literature on dual‐hedge strategies is based on a structured model to reduce roll‐over risk and is somehow difficult to apply for agricultural futures contracts. Instead, we propose to apply a regression based model and a naive rules of thumb for dual‐hedges which are applicable for agricultural commodities. The naive dual strategy stems from the fact that in a large sample of agricultural commodities, De Ville, Dhaene and Sercu (2008) find that GARCH‐based hedges do not perform as well as OLS‐based ones and that we can avoid estimation error with such a simple rule. Our semi‐naive hedge ratios are driven from two conditions: omitting exposure to spot price and minimising the variance of the unexpected basis effects on the portfolio values. We find that, generally, (i) rebalancing helps; (ii) the two‐contract hedging rules do better than the one‐contract counterparts, even for standard delta hedges without rolling‐over; (iii) simplicity pays: the naive rules are the best one–for corn and wheat within the two‐contract group, the semi‐naive rule systematically beats the others and GARCH performs worse than OLS for either one‐contract or two‐contract hedges and for soybeans the traditional naive rule performs nearly as well as OLS. These conclusions are based on the tests on unconditional variance ( Diebold and Mariano, 1995 ) and those on conditional risk ( Giacomini and White, 2006 ).     

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.     

Can Bonus‐Malus Allieviate Insurance Fraud?

Traditionally, insurance companies attempt to reduce (or even eliminate) fraud via audit strategies under which claims may be investigated at some cost to the insurer, with a penalty imposed upon insureds who are found to report claims fraudulently. However, it is also clear that, in a multiperiod setting, bonus‐malus contracts (increases in subsequent premiums whenever a claim is presented) also provide an incentive against fraud. In this article, we consider a model in which, conditional upon the client renewing his contract, the only mechanism used to combat fraud is bonus‐malus. In this way, our model provides the opposite pole to the pure audit model. We show that in our simplified setting there exists a bonus‐malus contract that will eliminate all fraud in all periods, while guaranteeing nonnegative expected profits to the insurer and participation by the insured. We also consider the dynamics of the solution, the effect of an increase in risk aversion on the solution, and the welfare implications.     

Development and Pricing of a New Participating Contract

Abstract

This article designs and prices a new type of participating life insurance contract. Participating contracts are popular in the United States and European countries. They present many different covenants and depend on national regulations. In the present article we design a new type of participating contract very similar to the one considered in other studies, but with the guaranteed rate matching the return of a government bond. We prove that this new type of contract can be valued in closed form when interest rates are stochastic and when the company can default.     

Risk Measurement Performance of Alternative Distribution Functions

This paper evaluates the performance of three extreme value distributions, i.e., generalized Pareto distribution (GPD), generalized extreme value distribution (GEV), and Box‐Cox‐GEV, and four skewed fat‐tailed distributions, i.e., skewed generalized error distribution (SGED), skewed generalized t (SGT), exponential generalized beta of the second kind (EGB2), and inverse hyperbolic sign (IHS) in estimating conditional and unconditional value at risk (VaR) thresholds. The results provide strong evidence that the SGT, EGB2, and IHS distributions perform as well as the more specialized extreme value distributions in modeling the tail behavior of portfolio returns. All three distributions produce similar VaR thresholds and perform better than the SGED and the normal distribution in approximating the extreme tails of the return distribution. The conditional coverage and the out‐of‐sample performance tests show that the actual VaR thresholds are time varying to a degree not captured by unconditional VaR measures. In light of the fact that VaR type measures are employed in many different types of financial and insurance applications including the determination of capital requirements, capital reserves, the setting of insurance deductibles, the setting of reinsurance cedance levels, as well as the estimation of expected claims and expected losses, these results are important to financial managers, actuaries, and insurance practitioners.     

Leading Indicator Variables, Performance Measurement, and Long-Term Versus Short-Term Contracts

In this article we develop a multiperiod agency model to study the role of leading indicator variables in managerial performance measures. In addition to the familiar moral hazard problem, the principal faces the task of motivating a manager to undertake “soft” investments. These investments are not directly contractible, but the principal can instead rely on leading indicator variables that provide a noisy forecast of the investment returns to be received in future periods. Our analysis relates the role of leading indicator variables to the duration of the manager's incentive contract. With short‐term contracts, leading indicator variables are essential in mitigating a holdup problem resulting from the fact that investments are sunk at the end of the first period. With long‐term contracts, leading indicator variables will be valuable if the manager's compensation schemes are not stationary over time. The leading indicator variables then become an instrument for matching the future investment return with the current investment expenditure. We identify conditions under which the optimal long‐term contract induces larger investments and less reliance on the leading indicator variables as compared with short‐term contracts. Under certain conditions, though, the principal does better with a sequence of one‐period contracts than with a long‐term contract.     

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.     

Types of dependence and time-dependent association between two lifetimes in single parameter copula models

Spreeuw, J. Types of dependence and time-dependent association between two lifetimes in single parameter copula models. Scandinavian Actuarial Journal. Most publications on modeling insurance contracts on two lives, assuming dependence of the two lifetimes involved, focus on the time of inception of the contract. The dependence between the lifetimes is usually modeled through a copula and the effect of this dependence on the pricing of a joint life policy is measured. This paper investigates the effect of association at the outset on the mortality in the future. The conditional law of mortality of an individual, given his survival and given the life status of the partner is derived. The conditional joint survival distribution of a couple at any duration, given that the two lives are then alive, is also derived. We analyze how the degree of dependence between the two members of a couple varies throughout the duration of a contract. We have done that for (mainly Archimedean) copula models, with one parameter for the degree of dependence. The conditional distributions hence derived provide the basis for the calculation of prospective provisions.     

保险合同的一些法律问题

我国保险法研究尚处于发展阶段,有关保险合同问题的认识比较混乱.本文针对争论比较多的保险合同的特征、保险合同中的要约与承诺、保险合同的形式以及保险利益等四个问题展开分析和讨论.文中充分利用了已有的研究成果,通过对比发现一些问题,并结合司法实践对相关问题进行再认识,从而提出了一些新的观点.     

A Finite Difference Approach to the Valuation of Path Dependent Life Insurance Liabilities

This paper sets up a model for the valuation of traditional participating life insurance policies. These claims are characterized by their explicit interest rate guarantees and by various embedded option elements, such as bonus and surrender options. Owing to the structure of these contracts, the theory of contingent claims pricing is a particularly well-suited framework for the analysis of their valuation.The eventual benefits (or pay-offs) from the contracts considered crucially depend on the history of returns on the insurance company's assets during the contract period. This path-dependence prohibits the derivation of closed-form valuation formulas but we demonstrate that the dimensionality of the problem can be reduced to allow for the development and implementation of a finite difference algorithm for fast and accurate numerical evaluation of the contracts. We also demonstrate how the fundamental financial model can be extended to allow for mortality risk and we provide a wide range of numerical pricing results.     

Competitive risk sharing contracts with one-sided commitment

This paper analyzes dynamic equilibrium risk sharing contracts between profit-maximizing intermediaries and a large pool of ex ante identical agents that face idiosyncratic income uncertainty that makes them heterogeneous ex post. In any given period, after having observed her income, the agent can walk away from the contract, while the intermediary cannot, i.e. there is one-sided commitment. We consider the extreme scenario that the agents face no costs to walking away, and can sign up with any competing intermediary without any reputational losses. We demonstrate that not only autarky, but also partial and full insurance can obtain, depending on the relative patience of agents and financial intermediaries. Insurance can be provided because in an equilibrium contract an up-front payment effectively locks in the agent with an intermediary. We then show that our contract economy is equivalent to a consumption-savings economy with one-period Arrow securities and a short-sale constraint, similar to Bulow and Rogoff [1989. Sovereign debt: is to forgive to forget? American Economic Review 79, 43-50]. From this equivalence and our characterization of dynamic contracts it immediately follows that without cost of switching financial intermediaries debt contracts are not sustainable, even though a risk allocation superior to autarky can be achieved.     

Creating Customer Value in Participating Life Insurance

The value of a life insurance contract may differ depending on whether it is looked at from the customer's point of view or that of the insurance company. We assume that the insurer is able to replicate the life insurance contract's cash flows via assets traded on the capital market and can hence apply risk‐neutral valuation techniques. The policyholder, on the other hand, will take risk preferences and diversification opportunities into account when placing a value on that same contract. Customer value is represented by policyholder willingness to pay and depends on the contract parameters, that is, the guaranteed interest rate and the annual and terminal surplus participation rate. The aim of this article is to analyze and compare these two perspectives. In particular, we identify contract parameter combinations that—while keeping the contract value fixed for the insurer—maximize customer value. In addition, we derive explicit expressions for a selection of specific cases. Our results suggest that a customer segmentation in this sense, that is, based on the different ways customers evaluate life insurance contracts and embedded investment guarantees while ensuring fair values, is worthwhile for insurance companies as doing so can result in substantial increases in policyholder willingness to pay.     

Unconditional Tests of Linear Asset Pricing Models with Time‐Varying Betas

In conditional affine factor models, estimated risk prices should satisfy certain unconditional constraints. Specifically, a cross‐sectional estimate of the unconditional slope associated with a risk factor should equal the average price of risk of the factor. The estimated slope associated with the product of a risk factor and an instrument should be equal to the covariance of the factor risk premium with the instrument. We show that the constraints only apply to the conditional models with time‐varying betas. We identify an unconditional constraint on unconditional betas for time‐varying beta models and incorporate it into model tests. We show that imposing this unconditional constraint changes estimates of unconditional betas and risk prices significantly.     

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.     

论财产保险合同的转让——兼评我国新《保险法》第49条

财产流转在现代社会中十分频繁,财产保险作为流转安全之保障如果不能随财产流转,就会产生很多问题。现实生活中,因财产保险合同转让产生的纠纷众多。本文由案例所涉及的问题,论述了保险利益对财产保险合同转让的影响;在此基础上,对我国新《保险法》中关于财产保险合同转让的规定进行了评析,并对其中的不足提出了一些完善的建议。     

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.     

Adverse Selection in a Model of Real Estate Lending

We provide a rationale for the presence of points in mortgage loan contracts. Our analysis builds on two key features. First, insurance markets are unavailable for labor income. Second, the “due-on-sale” clause allows banks to offer loan contracts which partially insure against fluctuations in labor income. If explicit prepayment penalties are prohibited by law, points serve effectively as prepayment penalties. We also examine environments where such penalties are not prohibited and show that points will be used if interest rates cannot depend on the size of the loan.