Some mathematical aspects of price optimisation

Calculation of an optimal tariff is a principal challenge for pricing actuaries. In this contribution we are concerned with the renewal insurance business discussing various mathematical aspects of calculation of an optimal renewal tariff. Our motivation comes from two important actuarial tasks, namely (a) construction of an optimal renewal tariff subject to business and technical constraints, and (b) determination of an optimal allocation of certain premium loadings. We consider both continuous and discrete optimisation and then present several algorithmic suboptimal solutions. Additionally, we explore some simulation techniques. Several illustrative examples show both the complexity and the importance of the optimisation approach.     

Directors' and officers' liability insurance and stock price crash risk

We investigate the impact of directors' and officers' insurance (D&O insurance) on stock price crash risk. We find that D&O insurance in China is negatively associated with stock price crash risk. This association is robust to a series of robustness checks including the use of alternative sample, Heckman two-step sample selection model, propensity score matching procedure, fixed effects model, the inclusion of some possibly omitted variables, and bootstrap method. Further analyses show that the impact of D&O insurance on crash risk is more pronounced in firms with lower board independence, non-Big 4 auditors, lower institutional shareholdings, and weaker investor protection; and the negative relationship between D&O insurance and crash risk is not driven by the eyeball effect. Moreover, we find that D&O insurance purchase is associated with less financial restatements and more disclosure of corporate social responsibility reports. Our findings provide support to the notion that D&O insurance appears to improve corporate governance.     

医疗保险定额付费方式有效性的探讨

医疗保险中的定额付费方式指不论实际发生了多少医疗费用,均以事先确定的标准向医疗机构支付费用,这种支付方式的有效运作意味着可以在控制医疗费用的同时又确保医疗质量.本文认为可能对定额付费方式有效性产生影响的因素包括服务质量对患者诊疗需求的影响程度;医疗机构增加患者诊疗需求的意愿;医疗机构的拒诊和撇脂行为;经办机构在合同签订...     

Understanding price competition in the German motor insurance market

This paper analyzes price competition in the German motor insurance market since 1994 and looks for evidence to back up a claim frequently found in the trade literature—that there have been two recent price wars in this industry, the first in 1996–1999, the second in 2005–2006. In a first step, we analyze the development of the German motor insurance market and compare it to that of other property-liability lines of business. In a second step the applicability of price war definitions found in the marketing literature to the German motor insurance market is checked. In a third step, a comparison to reference cases from other industries, where price wars have been subject to academic analysis, is conducted to complement the analysis. We conclude that, contrary to reports in the trade literature, the periods of 1996–1999 and 2005–2006 should be considered as times of intense competition in the motor insurance industry, not as times of price war.     

财险市场价格竞争有效性研究

我国国内财产保险业务自1980年恢复以来虽然取得了很大成绩,但依旧存在较多问题,特别是市场集中度偏高,导致市场竞争长期处于低水平竞争状态。本文根据市场份额将我国财险公司划分为在位者与竞争者两类,应用Stackelberg博弈模型,对在位者与竞争者的保险价格竞争从单时期和多时期两个层次进行分析,得出在财险市场中,单纯的价格竞争是无效的,并建议从产品和服务的创新、投资、成本管理和客户信息搜集与管理四方面协助价格竞争的展开。     

有限理性的价格认识在保险消费中的作用

保险产品本身的特殊性和复杂性以及消费者自身的心理因素,使得消费者在保险价格认识中仅具有有限理性。有限理性的价格认识使消费者在保险消费决策中难以做出主动购买的决策,并容易盲目购买低价产品,使市场总保险需求的价格敏感度较低,并使价格在财产保险消费中的作用大于在人身保险中的作用。保险企业应该有针对性地采取价格策略和相应的营销支持,使消费者对价格的认识成为促进保险产品销售的手段而不是障碍。     

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.     

The price,quality and distribution of mortgage payment protection insurance: A hedonic pricing approach

Mortgage payment protection insurance (hereafter MPPI) provides varying combinations of accident, sickness and unemployment insurance and is used to protect the mortgage payments of policyholders in the event of a fall in income. Despite alleviating housing market failures, this service has been heavily criticised for providing poor value for money and being associated with unhelpful sales techniques especially when sold jointly with a mortgage in the UK. Consequently, the Competition Commission (2009) ruled that after February 2011 MPPI should not be sold jointly with mortgage lending within seven days of the credit transaction. We examine whether this prohibition was justified and if the form of distribution, either jointly with the mortgage or independently influences the premium levels. This assessment uses a hedonic pricing approach with details and premiums of MPPI policies in 2010 and 2012. Despite the success in reducing MPPI premium levels, we conclude that the Competition Commission judgement has raised concerns as to mortgagee protection.     

Real-time revenue and firm disclosure

Review of Accounting Studies - We examine firm disclosure choice when information is received on a real-time, continuous basis. We use transaction-level credit and debit card sales for a sample of...     

论信用保险项下重复保险制度的构建

信用保险在我国是一个新兴的保险种类,根据我国《保险法》对于保险的基本分类,信用保险属于财产保险的一种,但实际上信用保险较之一般的财产保险存在诸多特殊之处,特别是在重复保险问题上更是难以适用《保险法》针对财产保险所设计的相关制度,同时,也不能按照人身保险生命无价原理确定和解决重复保险问题。当信用保险市场开放时,各保险人就会面对重复保险如何界定和分担责任的问题。本文对这一问题提出了一些解决思路。     

Non-rating revenue and conflicts of interest

Rating agencies produce ratings used by investors, but obtain most of their revenue from issuers, leading to a conflict of interest. We employ a unique data set on the use of non-rating services, and the associated payments, in India, to test if this conflict affects ratings quality. Agencies rate issuers that pay them for non-rating services higher (than agencies not hired for such services). Such issuers also have higher default rates. Both effects are increasing in the amount paid. These results suggest that issuers which hire agencies for non-rating services receive higher ratings despite having higher default risk.     

The interactive effect of revenue diversification and economic base on US local government revenue stability

Over the past 50 years, revenue diversification has emerged as an important trend in US local and state government finance. As a result, the role of the property tax has declined relative to other revenues, such as income taxes, sales taxes and user charges. This article examines the impact of revenue diversification on the revenue stability of local governments and whether the impact varies according to the nature of a jurisdiction's economic base. The findings are highly relevant to autonomous national governments in the EU. In addition, revenue stability is a significant factor that rating agencies take into account when determining a government's capacity to pay off debt, so the article has particular relevance to countries with large debts.     

Reinforcement learning and stochastic optimisation

At the heart of financial mathematics lie stochastic optimisation problems. Traditional approaches to solving such problems, while applicable to broad classes of models, require specifying a model to complete the analysis and obtain implementable results. Even then, the curse of dimensionality challenges the viability of conventional methods to settings of practical relevance. In contrast, machine learning, and reinforcement learning (RL) particularly, promises to learn from data and overcome the curse of dimensionality simultaneously. This article touches on several approaches in the extant literature that are well positioned to merge our traditional techniques with RL.

     

Social insurance for work and product injuries

Geneva Risk Economics Lecture, delivered at Centre HEC-ISA, Jouy-en-Josas, France, on September 18, 1989. The author would like to thank Eric Briys and Pascale Viala for both their helpful comments and their hospitality.     

Financing and the demand for corporate insurance

In this paper we examine the insurance decision of a firm with private information regarding its cash flows and insurable losses. We show that, even in the absence of bankruptcy costs and information production by insurers, the firm's attempts to hedge its information risk can induce it to demand insurance. If higher operating revenues are accompanied by a lower insurance risk, the firm will choose to self-insure. In contrast, if higher operating revenues are accompanied by a higher insurance risk, the firm will demand insurance. In fact, if its insurable losses are relatively small, the firm will fully insure its losses. Further, if there exists considerable uncertainty regarding the firm's insurance risk, the level of coverage demanded by the firm is dependent on its private information, with higher levels of coverage signaling favorable information regarding the firm's future operations.     

Implications of domestic price insulation for global food price behavior

Rapid changes in global food prices in recent years are widely viewed as a serious threat to global development. While various sources of price instability in agriculture have been identified, little attention appears to have been given to the importance of changes in trade policies that insulate domestic prices from world markets as a source of volatility in world prices. A contribution of this paper is to show that these interventions are dynamically more complex than simple proportional insulation. Insulation against an initial price increase in world prices increases the magnitude of that increase, while subsequent adjustments to the level of protection change the fundamental nature of price volatility. We find such policies are widespread and increase the volatility of world prices while not reducing the volatility of domestic prices because of the collective action problem involved in this form of policy intervention.     

Structural and executional drivers of downstream revenue

Revenue flows that occur at other related organizational units and over time are an important part of customer profitability analysis and resource planning. This study analyzes downstream revenue generated from establishing a series of additional organizational units. The setting is a central hospital which established a group of specialty outreach clinics. Using a specially-collected time-series database I show two distinct patterns, depending on the clinic's specialty. One type triggers immediate incremental downstream revenue to the clinic's sponsoring department. The other type of clinic generates revenue that is smaller in value, later in time and mostly in departments not associated with the sponsoring department's medical specialty. Structural and executional clinic characteristics such as distance and clinic frequency differentially affect the amount of revenue generated, implying a need for tailoring performance measures to “clinic type”. Overall, my results suggest caution in developing performance measures that include financial impact in other organizational units – context matters even in a relatively homogenous setting of specialty clinics in one hospital system.