Pricing Dynamic Insurance Risks Using the Principle of Equivalent Utility

We introduce an expected utility approach to price insurance risks in a dynamic financial market setting. The valuation method is based on comparing the maximal expected utility functions with and without incorporating the insurance product, as in the classical principle of equivalent utility. The pricing mechanism relies heavily on risk preferences and yields two reservation prices - one each for the underwriter and buyer of the contract. The framework is rather general and applies to a number of applications that we extensively analyze.     

Efficient Pricing of Ratchet Equity-Indexed Annuities in a Variance-Gamma Economy

Abstract

In this paper we propose a new method for approximating the price of arithmetic Asian options in a Variance-Gamma (VG) economy, which is then applied to the problem of pricing equityindexed annuity contracts. The proposed procedure is an extension to the case of a VG-based model of the moment-matching method developed by Turnbull and Wakeman and Levy for the pricing of this class of path-dependent options in the traditional Black-Scholes setting. The accuracy of the approximation is analyzed against RQMC estimates for the case of ratchet equityindexed annuities with index averaging.     

Insurance Pricing,Reserving, and Performance Evaluation Under External Constraints on Capitalization and Return on Equity

We derive formulas for calculating the premiums that should be charged on policies in a discounted cash flow model with tax reserves and required assets that are determined by regulation. We also determine the unique division of required assets into “reserves” and “capital” that allows the product profitability to be correctly evaluated. That is, the profit after capital charges is zero if the product achieves the return assumed in pricing. We illustrate the concepts using whole life insurance and guaranteed minimum death benefit examples.     

大数据背景下的寿险产品定价与创新

本文主要探讨大数据对保险业的影响,并以实例说明在大数据背景下传统寿险产品定价的改进以及新型保险产品的开发情况。首先基于实际数据对于保险业大数据现状进行了统计分析,给出了保险业数据量现状以及数据使用效率的统计结果;其次以实际大数据量为基础,对传统的寿险产品定价进行了改进,获得了更优的市场比较优势;最后,以大数据量为基础,打破传统寿险产品的思维定式,开发出新型的保险产品并对产品风险进行了精确测定。     

Pricing Asian Options and Equity-Indexed Annuities with Regime Switching by the Trinomial Tree Method

Abstract

Equity-indexed annuities (EIAs) provide investors with a minimum rate of return and at the same time the opportunity of gaining a profit that is linked to the performance of an equity index. These properties make EIAs a popular product in the market. For modeling the equity index process and calculating the price of EIAs, as the maturity of EIAs usually is long, it is more reasonable to assume that the interest rate and the volatility of the equity index are stochastic processes. One simple way is to apply the regime-switching model, which allows these parameters depending on the market situation. However, the valuation of derivatives in such models is challenging, especially for the strong path-dependent options such as Asian options. A trinomial tree model is introduced to provide an efficient way to solve this problem. The valuation of Asian options is studied and extended to Asian-option-related EIAs.     

Cybersecurity Insurance: Modeling and Pricing

Cybersecurity risk has attracted considerable attention in recent decades. However, the modeling of cybersecurity risk is still in its infancy, mainly because of its unique characteristics. In this study, we develop a framework for modeling and pricing cybersecurity risk. The proposed model consists of three components: the epidemic model, loss function, and premium strategy. We study the dynamic upper bounds for the infection probabilities based on both Markov and non-Markov models. A simulation approach is proposed to compute the premium for cybersecurity risk for practical use. The effects of different infection distributions and dependence among infection processes on the losses are also studied.     

Performance Management in Insurance Firms by Using Transfer Pricing

In this article, we analyze the asset and liability management and market risk systems of insurance companies. We discuss that the current system is not goal congruent and does not satisfy necessary conditions for effective control. It follows that managers are unable to run their business effectively. We develop a transfer pricing system that allows the clear separation of underwriting and investment activities, both on the risk and return aspects. It creates the appropriate incentive schemes. We illustrate this system with an example indicating the differences in incentives between the traditional embedded value measures and the proposed funds transfer pricing system.     

长寿风险对寿险和年金产品定价的对冲效应研究

作为老龄社会的重要风险,长寿风险专题研究是近20年来公共养老金领域、保险公司关注的热点。长寿风险引发的保险公司寿险产品定价高估和年金产品定价低估之间存在潜在的自然对冲效应。为了量化这种对冲效应的长期影响,本文基于构建的同时涵盖低龄、高龄和超高龄在内的整个生命跨度的全年龄人口动态死亡率模型,采用对冲弹性量化终身寿险与终身年金、两全保险与定期年金、递延寿险与递延年金三类保障型寿险产品和养老型年金产品对冲效应的动态演变,并通过敏感性分析扩展探讨利率变化对对冲效应的长期影响。研究发现,从单位寿险和年金产品组合的净对冲效应来看,由于保险公司的产品定价区分了性别差异,使得女性的对冲效应更明显,因而女性对应的产品组合中的长寿风险对保险公司的影响更不显著。作为系统性风险,利率风险和长寿风险也存在对冲,利率上升能抵消或对冲长寿风险的影响,低利率下长寿风险更显著。     

利率市场化和寿险定价利率改革互动研究

随着我国利率市场化的深入推进,寿险定价利率市场化呼之欲出。本文从分析部分国家利率市场化和寿险定价利率市场化互动及影响入手,在总结利率市场化和寿险定价利率市场化的互动对寿险市场影响的基础上,分析了2011年以来我国利率市场化启动对我国寿险市场带来的挑战,并从监管、市场机制和保险公司自身等角度提出了应对挑战的建议。     

存款保险定价研究:期权定价法和预期损失定价法的进展

合理的存款保险定价可有效减少道德风险和逆向选择问题。本文梳理了国内外关于存款保险定价的两种主要方法——期权定价法和预期损失定价法及其最新发展情况。期权定价法的核心是将存款保险看作存款保险机构以银行资产为标的发行的一份看跌期权,之后学者从股利发放、监管宽容、系统性风险等多个角度进行拓展。预期损失定价法主要根据边际损失与边际保费收入相等来进行保费厘定,以探寻如何通过更科学的方法更精确地测量银行的预期损失。此外,本文讨论了存款保险定价方法对我国的启示。     

Overview of Reserving Practices for Substandard Life Policies

Abstract

This paper reviews the various industry practices, both past and current, for determining statutory reserves for substandard life insurance policies This review begins with single-life policies but also considers the application of single-life practice to joint-life policies The increased popularity of joint-life policies has taken place without much discussion in the technical journals of how to handle such issues as reserves on substandard business. This paper is intended to provoke such a discussion and to provide a framework for it.     

Market Pricing of Deposit Insurance

We provide an approach to the market valuation of deposit insurance that is based on reduced-form methods for the pricing of fixed-income securities under default risk. By reference to bank debt prices as well as qualitative-response models of the probability of bank failure, we suggest how a risk-neutral valuation model for deposit insurance can be applied both to the calculation of fair-market deposit insurance premia and to the valuation of long-term claims against the insurer.     

Deposit Insurance and the Discount Window: Pricing under Asymmetric Information

The risk-sensitive pricing of deposit insurance and the discount window is determined in an environment where banks have private information concerning their financial conditions. The two facilities are managed jointly; an incentive-compatible policy is designed such that banks' choice of terms at which they can obtain insurance and access to discount window credit will reveal their asset quality. The function of the discount window is to be a risk-neutral “lender of last resort” to banks in a market dominated by risk-averse depositors.     

Arbitrage Pricing Theory and Utility Stock Returns

This paper presents some new evidence that Arbitrage Pricing Theory may lead to different and better estimates of expected return than the Capital Asset Pricing Model, particularly in the case of utility stock returns. Results for monthly portfolio returns for 1971–1979 lead to the conclusion that regulators should not adopt the single-factor risk approach of the CAPM as the principal measure of risk, but give greater weight to APT, whose multiple factors provide a better indication of asset risk and a better estimate of expected return.     

寿险公司适用弃权与禁止反言原则的影响与对策

新保险法修订,其突出要点之一在于强化了对投保人、被保险人利益的保护.增加弃权与禁止反言原则,是新修订保险法的一大亮点.本文研究的主旨是通过分析弃权与禁止反言原则意义,提出对寿险业的影响,分析所产生的新趋势,从而提出寿险公司适用弃权与禁止反言原则的对策.     

Using Parametric Bootstrap to Introduce and Manage Uncertainty: Replicated Loaded Insurance Life Tables

Insurance companies develop loaded life tables to protect themselves against deviations, for example, in the number of expected deaths or in the (residual) expectation of life of their insured. In doing so, however, the single random vector of experience crude death rates from which loaded tables are constructed is treated as deterministic or, at best, as a single realization of an underlying stochastic process, omitting the fact that it is estimated and subject to error and uncertainty. This can result in serious consequences for the insurer. To solve this problem, we follow the example of other researchers and propose a method to replicate loaded life tables using parametric bootstrap. We focus on estimating period-loaded life tables from company portfolios, where the sizes of the exposed-to-risk populations are significantly smaller than those of general populations. If we have a set of B loaded life tables, the average behavior and some extreme values can be computed and subsequently used in managing premiums or reserves. This article offers life insurers a simple way of incorporating the experience uncertainty in actuarial tasks (for example, in pricing) by comparing the limits of the confidence intervals obtained between parametric bootstrap and classical approaches (such as limit theorems).     

Pricing Risk-Adjusted Deposit Insurance: An Option-Based Model

This paper presents a methodology for arriving at empirical estimates of deposit insurance premiums from market data by using isomorphic relationships between equity and a call option, and insurance and a put option. The data utilizes the market value of equity to solve for the asset value and its volatility. Market perceptions of FDIC bailout policies are explicitly modeled so as to eliminate the bias in inverted values of assets and their volatility. Sensitivity analyses are performed to show that rank orderings based on premiums are robust to changes in specification, thus facilitating allocation of aggregate premium across banks.     

Long-Term Care Insurance and Life Insurance Demand

This article investigates the interaction between life insurance and long-term care insurance markets on the demand side. In the model utility depends on both consumption and bequest, and utility from consumption is contingent on the state of health. While the demand for life insurance increases both with decreasing income and with a rising degree of altruism, the influences of these two parameters on the demand for long-term care insurance are ambiguous. If the utility shock arising from disability declines, both insurance demands will rise.     

Asset Pricing of Insurance Loss Liabilities: Some Examples

I construct examples of valuing insurance loss liabilities with asset pricing models, comparing the Rubinstein‐Leland model with the better‐known CAPM. The two models give different values only if the loss payment is asymmetric and correlated with the market portfolio, conditions which can result from the nature of the underlying loss or from the impact of insolvency on the insurer's payment.
In examples where insolvency is not possible and there is no liquidity cost of raising new equity on short notice, the value of a loss liability is equal to the value of the underlying loss, i.e., of the promised coverage, and depends neither on (1) the size of the loss pool; nor on (2) the unsystematic risk of the insurer's liabilities; nor on (3) the composition of an insurer's investment portfolio; nor on (4) the amount of insurer equity.
These factors do affect the value of a loss liability in examples where insolvency and liquidity costs are considered. Other things equal, if a factor increases the likelihood of insolvency, the fair value of a loss liability is lower because the insured is partially self‐insuring; but the liquidity cost of maintaining solvency by raising new equity on short notice is higher, implying a higher fair value of the loss liability.