Home Equity Insurance

Home equity insurance policies—policies insuring homeowners against declines in the prices of their homes—would bear some resemblance both to ordinary insurance and to financial hedging vehicles. A menu of choices for the design of such policies is presented here, and conceptual issues are discussed. Choices include pass-through futures and options, in which the insurance company in effect serves as a retailer to homeowners of short positions in real estate futures markets or of put options on real estate indices. Another choice is a life-event-triggered insurance policy, in which the homeowner pays regular fixed insurance premia and is entitled to a claim if both a sufficient decline in the real estate price index and a specified life event (such as a move beyond a certain geographical distance) occur. Pricing of the premia to cover loss experience is derived, and tables of break-even policy premia are shown, based on estimated models of Los Angeles housing prices from 1971 to 1994.     

Insurance ratemaking using a copula-based multivariate Tweedie model

The Tweedie distribution, featured with a mass probability at zero, is a convenient tool for insurance claims modeling and pure premium determination in general insurance. Motivated by the fact that an insurance policy typically provides multiple types of coverage, we propose a copula-based multivariate Tweedie regression for modeling the semi-continuous claims while accommodating the association among different types. The proposed approach also allows for dispersion modeling, resulting in a multivariate version of the double generalized linear model. We demonstrate the application in insurance ratemaking using a portfolio of policyholders of automobile insurance from the state of Massachusetts in the United States.     

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.     

Survival Analysis of a Household Portfolio of Insurance Policies: How Much Time Do You Have to Stop Total Customer Defection?

Customer‐side influences on insurance have been relatively ignored in the literature. Using the household as the unit of analysis, this article focuses on the behavior of households having multiple policies of different types with the same insurance company, and who cancel their first policy. How long after the household's cancellation of the first policy does the insurer have to retain the customer and avoid customer defection on all policies to the competition? And, what customer characteristics are associated with customer loyalty? Using logistic regression and survival analysis techniques, an assessment is made of the probability of total customer withdrawal, and the length of time between first cancellation and subsequent customer withdrawal. Using a European database spanning 54 months of household multiple policyholder behavior, the results show that cancellation of one policy is a very strong indicator that other household policies will be canceled. Further, the insurer can have time to react to retain the customer after the first cancellation, however, this time is significantly dependent on the method used to contact the company, household demographics, and the nature of the household's insurance policy portfolio. Surprisingly, core customers having three or more policies in addition to the canceled policy are more vulnerable to total defection on all policies than noncore customers. Further, the potential customer repelling effects of premium increases seem to wear out after 12 months. Strategic implications of the results are presented.     

Guarantees in With-Profit and Unitized With-Profit Life Insurance Contracts: Fair Valuation Problem in Presence of the Default Option

The purpose of the article is to apply contingent claim theory to the valuation of the type of participating life insurance policies commonly sold in the UK. The article extends the techniques developed by Haberman, Ballotta, and Wang (2003) to allow for the default option. The default option is a feature of the design of these policies, which recognizes that the insurance company's liability is limited by the market value of the reference portfolio of assets underlying the policies that have been sold. The valuation approach is based on the classical contingent claim pricing “machinery,” underpinned by Monte Carlo techniques for the computation of fair values. The article addresses in particular the issue of a fair contract design for a complex type of participating policy and analyzes in detail the feasible set of policy design parameters that would lead to a fair contract and the trade‐offs between these parameters.     

Are Farmers’ Behaviors Rational When They Pay Less for Social Endowment Insurance? Evidence from Chinese Rural Survey Data

In recent years, farmers have had high participation rate in the rural social endowment insurance in China, for which personal contribution and government subsidy are the main funding source. There have been increasingly more farmers participating into the program. However, their enthusiasm for high premium payment was rather low as most of them selected the minimum premium for insurance. In this article, the discounted utility theory from behavioral economics was adopted to analyze insurance selection behaviors of farmers; in addition, a discounted incremental utility model with a hyperbolic discounting function was also further constructed to describe their insurance decision-making processes. Based on the investigation of time preferences of farmers, their insurance participation behaviors of diverse natures were simulated. The corresponding results indicated that active insurance participation and low insurance premium payment were rational choices for most farmers; in comparison, for the elders with higher income, different choices can be made. Therefore, policy makers could formulate differentiated subsidy policies directing at farmers from different groups, so as to stimulate their enthusiasm for premium payment.     

Longitudinal modeling of insurance claim counts using jitters

Modeling insurance claim counts is a critical component in the ratemaking process for property and casualty insurance. This article explores the usefulness of copulas to model the number of insurance claims for an individual policyholder within a longitudinal context. To address the limitations of copulas commonly attributed to multivariate discrete data, we adopt a ‘jittering’ method to the claim counts which has the effect of continuitizing the data. Elliptical copulas are proposed to accommodate the intertemporal nature of the ‘jittered’ claim counts and the unobservable subject-specific heterogeneity on the frequency of claims. Observable subject-specific effects are accounted in the model by using available covariate information through a regression model. The predictive distribution together with the corresponding credibility of claim frequency can be derived from the model for ratemaking and risk classification purposes. For empirical illustration, we analyze an unbalanced longitudinal dataset of claim counts observed from a portfolio of automobile insurance policies of a general insurer in Singapore. We further establish the validity of the calibrated copula model, and demonstrate that the copula with ‘jittering’ method outperforms standard count regression models.     

基于RAROC的保险基金投资策略研究

本文针对当前典型的保险基金投资策略模型的不足,结合当前金融风险管理和金融监管的主流方法,建立了同时考虑保费收取与赔付支出、破产概率、VaR限额的RAROC最大化模型,得到了最优的投资策略.在此基础上进行案例分析,讨论了索赔强度、保费收取率、个体赔付额度等因素的变化对该策略的影响.研究发现,保险公司必须根据承保状况及时调...     

Optimal Dynamic Premium Control in Non-life Insurance. Maximizing Dividend Pay-outs

In this paper we consider the problem of finding optimal dynamic premium policies in non-life insurance. The reserve of a company is modeled using the classical Cramér-Lundberg model with premium rates calculated via the expected value principle. The company controls dynamically the relative safety loading with the possibility of gaining or loosing customers. It distributes dividends according to a 'barrier strategy' and the objective of the company is to find an optimal premium policy and dividend barrier maximizing the expected total, discounted pay-out of dividends. In the case of exponential claim size distributions optimal controls are found on closed form, while for general claim size distributions a numerical scheme for approximations of the optimal control is derived. Based on the idea of De Vylder going back to the 1970s, the paper also investigates the possibilities of approximating the optimal control in the general case by using the closed form solution of an approximating problem with exponential claim size distributions.     

Who Obtains Greater Discounts on Automobile Insurance Premiums?

Insurance purchasers obtain varied discounts for insurance. This paper examines what drives these differences, specifically whether the loss probability and the wealth of the insured affect the size of the premium discount in automobile insurance. To describe a bargain between a client and an insurer over premiums and coverage, we first develop a sequential insurance bargaining game where the client has an outside option to bargain with another insurer. We find that the equilibrium involves full coverage and, based on the results of comparative statics, we propose hypotheses regarding the effects of the loss probability and the wealth of the insured on the size of the premium discount. We then use a unique data set of 85,806 observations of Taiwanese automobile liability insurance for property damage to empirically test the predictions. After controlling for underwriting and macroeconomic variables, we find that both (1) the insured with a lower claim probability (as a proxy for the insured with a lower loss probability) and (2) the insured with a higher salvage value car (as a proxy for the wealthier insured) receive a greater premium discount. These results support our theoretical results.     

Reinsurance premium principles based on weighted loss functions

ABSTRACT

In this paper, we propose new reinsurance premium principles that minimize the expected weighted loss functions and balance the trade-off between the reinsurer's shortfall risk and the insurer's risk exposure in a reinsurance contract. Random weighting factors are introduced in the weighted loss functions so that weighting factors are based on the underlying insurance risks. The resulting reinsurance premiums depend on both the loss covered by the reinsurer and the loss retained by the insurer. The proposed premiums provide new ways for pricing reinsurance contracts and controlling the risks of both the reinsurer and the insurer. As applications of the proposed principles, the modified expectile reinsurance principle and the modified quantile reinsurance principle are introduced and discussed in details. The properties of the new reinsurance premium principles are investigated. Finally, the comparisons between the new reinsurance premium principles and the classical expectile principle, the classical quantile principle, and the risk-adjusted principle are provided.     

商业健康险税收优惠政策的效果分析--基于需求价格弹性的测算

本文基于经典商业健康险需求理论的价格弹性模型,分别利用天津市调研数据和中山大学劳动力动态调查数据库测算了按收入分层的商业健康险需求价格弹性及商业健康险的消费结构。并基于上述测算结果,通过数据库对接推算了全国商业健康险的需求价格弹性和税优政策的预期效果。测算结果表明,我国商业健康险的需求价格弹性为-0.22,在当前的税优政策下,个税税改前后,税优健康险的预期年保费规模分别为16.54亿元、6.09亿元,由此带来的年税式支出预计将分别达到2.47亿元、0.69亿元。最后,基于实证分析结果,本文对税优健康险未来的政策调整方向提供了建议。     

Diversification and risk-adjusted performance: A quantile regression approach

The effect of diversification on firm performance has been debated. We reexamine the effect using a sample of 44,248 observations of non-financial US firms for the 1997–2009 period employing the quantile regression approach. Our empirical results show that the effect of diversification on firm performance is not homogeneous across various quantile levels: the diversification discount (premium) shows up in firms with high (low) RoE quantiles. Further, we find that diversification affects firm risk as well. Therefore, we consider a risk-adjusted performance measure and find that both diversification discount and premium disappear, which is consistent with the risk-return trade-off principle.     

The Equity Premium: Consistent with GDP Growth and Portfolio Insurance

We find that the long‐term equity premium is consistent with both GDP growth and portfolio insurance. We use a supply‐side growth model and demonstrate that the arithmetic average stock market return and the returns on corporate assets and debt depend on GDP per capita growth. The implied equity premium matches the U.S. historical average over 1926–2001. Separately, we find that the equity premium tracks the value of a put option on the S&P 500. Our theory predicts a smaller equity premium in the future, assuming that the recent regime shifts in dividend policies, interest rates, and tax rates are permanent.     

Equilibrium Pricing of General Insurance Policies

Abstract

A model is developed for determining the price of general insurance policies in a competitive, noncooperative market. This model extends previous single-optimizer pricing models by supposing that each participant chooses an optimal pricing strategy. Specifically, prices are determined by finding a Nash equilibrium of an N-player differential game. In the game, a demand law describes the relationship between policy sales and premium, and each insurer aims to maximize its (expected) utility of wealth at the end of the planning horizon. Two features of the model are investigated in detail: the effect of limited total demand for policies, and the uncertainty in the calculation of the breakeven (or cost price) of an insurance policy.

It is found that if the demand for policies is unlimited, then the equilibrium pricing strategy is identical for all insurers, and it can be found analytically for particular model parameterizations. However, if the demand for policies is limited, then, for entrants to a new line of business, there are additional asymmetric Nash equilibria with insurers alternating between maximal and minimal selling. Consequently it is proposed that the actuarial cycle is a result of price competition, limited demand, and entry of new insurers into the market. If the breakeven premium is highly volatile, then the symmetric equilibrium premium loading tends to a constant, and it is suggested that this will dampen the oscillatory pricing of new entrants.     

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.     

我国交强险索赔频率影响因素分析 ——基于GAM和广东、河南、湖北、山东的经验数据

为分析我国交强险各因素对索赔频率的影响,以2016年广东、河南、湖北、山东四省的保单数据为样本,采用广义可加模型（GAM）对其保单中的驾驶员年龄、汽车车龄和汽车重量进行非参数分析,并对公路里程数等变量进行参数分析。结果表明：索赔频率有明显的地区差异,公路里程数对索赔频率有正向的影响,其中除汽车车型对索赔频率没有影响外,其余变量均有显著影响。     

The Determination of Fair Profits for the Property-Liability Insurance Firm

Single period and dynamic valuation models in continuous time, under certainty and uncertainty, are developed for a property-liability insurance contract to determine the “fair” (competitive) premium and underwriting profit. The intertemporal stochastic model assumes that the claim frequency and the price index of claim settlements are functions of a set of underlying state variables which follow a multivariate Wiener process. The competitive premium is shown to be proportional to the claim frequency and the price index for claim settlements at the time the policy is issued. The factor of proportionality varies directly with the claim settlement rate and the length of coverage, and inversely with the risk-adjusted real interest rate on the dollar-valued claim rate.     

Quantile forecasts of daily exchange rate returns from forecasts of realized volatility

Quantile forecasts are central to risk management decisions because of the widespread use of Value-at-Risk. A quantile forecast is the product of two factors: the model used to forecast volatility, and the method of computing quantiles from the volatility forecasts. In this paper we calculate and evaluate quantile forecasts of the daily exchange rate returns of five currencies. The forecasting models that have been used in recent analyses of the predictability of daily realized volatility permit a comparison of the predictive power of different measures of intraday variation and intraday returns in forecasting exchange rate variability. The methods of computing quantile forecasts include making distributional assumptions for future daily returns as well as using the empirical distribution of predicted standardized returns with both rolling and recursive samples. Our main findings are that the Heterogenous Autoregressive model provides more accurate volatility and quantile forecasts for currencies which experience shifts in volatility, such as the Canadian dollar, and that the use of the empirical distribution to calculate quantiles can improve forecasts when there are shifts.     

保险资金的证券投资绩效分析

本文回顾了保险资金在证券投资领域的政策变化历程,分析了保险资金运用效率与基金业绩评价的诸多不同,指出了基于资产组合优化理论的保险资金评价方法的不足,提出用影子组合法,作为一种正向制度激励,对保险资金运用效率进行评价,并基于该方法对三家上市保险公司的资金运用效率进行了比较。