Regression-based algorithms for life insurance contracts with surrender guarantees

We present a general framework for pricing life insurance contracts embedding a surrender option. The model allows for several sources of risk, such as uncertainty in mortality, interest rates and other financial factors. We describe and compare two numerical schemes based on the Least Squares Monte Carlo method, emphasizing underlying modeling assumptions and computational issues.     

Corporate Hedging in the Insurance Industry

Abstract

In this paper we investigate the extent to which insurance companies utilize financial derivatives contracts in the management of risks The data set we employ allows us to observe the universe of individual insurer transactions for a class of contracts, namely, those normally thought of as off-balance-sheet (OBS) We provide information on the number of insurers using various types of derivatives contracts and the volume of transactions in terms of notional amounts and the number of counterparties. Life insurers are most active in interest rate and foreign exchange derivatives, while property/casualty insurers tend to be active in trading equity option and foreign exchange contracts Using a multivariate probtt analysis, we explore the factors that potentially influence the existence of OBS activities. We also investigate questions relating to whether certain subsets of OBS transactions (for example, exchange traded) are related to such things as interest rate risk measures, organizational form and other characteristics that may discriminate between desired risk/return profiles across a cross-section of insurers. We find evidence consistent with the use of derivatives by insurers to hedge risks posed by guaranteed investment contracts (GICs), coilater-alized mortgage obligations (CMOs), and other sources of financial risk     

Relative Importance of Risk Sources in Insurance Systems

Abstract

Actuaries, and other managers of uncertainty, identify factors in modeling insurance risks because they believe (1) that these factors affect the outcome of a risk or (2) that the factors can be managed, thus allowing analysts a degree of control over the insurance system. This paper shows how to use a statistical measure, the coefficient of determination, for quantifying the relative importance of a source of uncertainty. With a quantitative measure of relative importance, risk managers can sharpen their intuition about the relative importance of risk factors and become better custodians of financial security systems.

This paper shows that the coefficient of determination is intuitively appealing in assessing the effectiveness of basic risk management techniques including risk exchange, pooling, and financial risk management. A single source common to all risks reduces the effectiveness of a pool; the risk measure quantifies the relative importance of this common source. The coefficient of determination is shown to have roots in the economics as well as the statistics literature. This connection provides further motivation for using the coefficient of determination and also suggests alternative measures for quantifying relative importance. The risk measure is useful in multivariate situations in which several factors affect a risk simultaneously. The paper illustrates this usefulness by considering a pool of policies that is subject to mortality, a common disaster, and a common investment environment.     

Vergleich von ökonomischen und biometrischen Risiken in der Personenversicherung

In life insurance both the time and the amount of future payments between insurer and policyholder may be stochastic; biometrical as well as financial risks are transferred to the insurer. We present an approach that allows to decompose the randomness of the discounted value of future benefits and premiums to a sum whose addends correspond to the uncertainty of the policy development, the interest rates, the probabilities of death, the probabilities of disablement, etc. Upon modeling the actuarial assumptions stochastically, we quantify these risk factors for typical life insurance contracts and compare them with each other. Contrary to a common folklore, the examples show that the systematic biometrical risks are in many cases not marginal compared to the interest rate risk.     

A stochastic differential game for optimal investment of an insurer with regime switching

We introduce a model to discuss an optimal investment problem of an insurance company using a game theoretic approach. The model is general enough to include economic risk, financial risk, insurance risk, and model risk. The insurance company invests its surplus in a bond and a stock index. The interest rate of the bond is stochastic and depends on the state of an economy described by a continuous-time, finite-state, Markov chain. The stock index dynamics are governed by a Markov, regime-switching, geometric Brownian motion modulated by the chain. The company receives premiums and pays aggregate claims. Here the aggregate insurance claims process is modeled by either a Markov, regime-switching, random measure or a Markov, regime-switching, diffusion process modulated by the chain. We adopt a robust approach to model risk, or uncertainty, and generate a family of probability measures using a general approach for a measure change to incorporate model risk. In particular, we adopt a Girsanov transform for the regime-switching Markov chain to incorporate model risk in modeling economic risk by the Markov chain. The goal of the insurance company is to select an optimal investment strategy so as to maximize either the expected exponential utility of terminal wealth or the survival probability of the company in the ‘worst-case’ scenario. We formulate the optimal investment problems as two-player, zero-sum, stochastic differential games between the insurance company and the market. Verification theorems for the HJB solutions to the optimal investment problems are provided and explicit solutions for optimal strategies are obtained in some particular cases.     

Joint Insolvency Analysis of a Shared MAP Risk Process: A Capital Allocation Application

In recent years, multivariate insurance risk processes have received increasing attention in risk theory. First-passage-time problems in the context of these insurance risk processes are of primary interest for risk management purposes. In this article we study joint-ruin problems of two risk undertakers in a proportionally shared Markovian claim arrival process. Building on the existing work in the literature, joint-ruin–related quantities are thoroughly analyzed by capitalizing on existing results in certain univariate insurance surplus processes. Finally, an application is considered where the finite-time and infinite-time joint-ruin probabilities are used as risk measures to allocate risk capital among different business lines. The proposed joint-ruin allocation principle enables us to not only capture the risk dynamics over a given time horizon, but also overcome the “cross-subsidizing” effect of many existing allocation principles.     

Risk perception and risk management in the Middle East market: theory and practice of multinational enterprises in Saudi Arabia

This exploratory study investigates the risk perception and risk management strategies of Western multinational enterprises in the Middle East. A sample of 49 German companies operating in Saudi Arabia provides the empirical setting for this research. The study reveals that cultural risk is assessed as more important in the business environment than political, financial, and economic risk. The most critical risk factors are not sufficiently included in the methodology of country risk measures, which are often used as a source for country‐specific risk information. In terms of risk management strategies, participating firms use mostly informal approaches rather than structured hedging or insurance products. Furthermore, we find that firm size has implications on the perception of some risk factors and for the level of risk management sophistication.     

经济政策不确定性、地区文化与保险需求

本文在拓展背景风险理论研究的基础上,揭示了经济政策不确定性对保险需求的影响及其受地区文化制约的理论机制。并利用2007-2017年中国30个地区的月度面板数据,检验了经济政策不确定性、地区文化与保险需求间的内在联系。结果发现:第一,经济政策不确定性会对保险需求产生显著正影响,且这种效应在地区人身险需求上表现更明显;第二,将地区文化指标集纳入经济政策不确定性与保险需求关系的研究框架,发现地区文化差异会对经济政策不确定性影响保险需求产生调节效应。因此政府需在充分重视经济政策波动和文化对经济活动的双重影响基础上,加强国内社会保障体系建设,建立更透明的信息传递渠道,培育人们主动抵抗风险的意识和文化习惯,调整保险供给结构,以减少不确定性对社会经济行为的负面冲击。     

Optimal investment of an insurer with regime-switching and risk constraint

We investigate an optimal investment problem of an insurance company in the presence of risk constraint and regime-switching using a game theoretic approach. A dynamic risk constraint is considered where we constrain the uncertainty aversion to the ‘true’ model for financial risk at a given level. We describe the surplus of an insurance company using a general jump process, namely, a Markov-modulated random measure. The insurance company invests the surplus in a risky financial asset whose dynamics are modeled by a regime-switching geometric Brownian motion. To incorporate model uncertainty, we consider a robust approach, where a family of probability measures is cosidered and the insurance company maximizes the expected utility of terminal wealth in the ‘worst-case’ probability scenario. The optimal investment problem is then formulated as a constrained two-player, zero-sum, stochastic differential game between the insurance company and the market. Different from the other works in the literature, our technique is to transform the problem into a deterministic differential game first, in order to obtain the optimal strategy of the game problem explicitly.     

Interest-risk sensitive deposit insurance premia: Stable ACH estimates

The parameters of interest rate uncertainty are estimated by maximum likelihood for the period 1952–1982, and used to evaluate bank or thrift deposit insurance as a function of duration mismatching, capital/asset ratio, and the recent history of interest rate forecasting errors. Homoskedasticity is overwhelmingly rejected in favor of adaptive conditional heteroskedasticity (ACH). Even after removing this heteroskedasticity, normality gives much lower likelihood than Paretian stable distributions with characteristic exponent in the range 1.614 to 1.714. The conditional deposit insurance values fluctuate by factors in excess of 300 for some duration gaps over the past three decades.     

Roland W. Scholz: Environmental Literacy in Science and Society. From Knowledge to Decisions. Cambridge University Press 2011

This study pursues the following aims: to examine how news stories use frames, emotions, and uncertainty to present environmental risk information; to identify which aspects of risk issues they highlight; and to analyze how these stories’ representations of risk and uncertainty might differ according to the sources they use. Content analysis of 641 news stories in South Korea over the last decade yields three findings: (1) reassurance was the most frequently used news frame, while uncertainty and emotion were used less often than expected; (2) news stories using government/industry/experts as sources vs. activists/lay people highlighted different news frames and risk information; and (3) the two most frequently used uncertainty presentation formats were single point estimate and verbal estimate. This study contributes to existing literature on the roles of media in environmental risk communication in two ways. First, it examines the specific formats journalists use to present uncertainty about risks. Second, it integrates news frames with the emotional characteristics of risk communication and with differences in risk information characteristics according to source. Implications are discussed regarding how a better understanding of news representations of risk could inform and enhance cooperation between experts and journalists, and lead to more effective environmental risk communication. Finally, this content analysis provides a stepping stone for future research that could further investigate and test how publics respond to risk messages that have varying permutations of emotional content and risk presentation formats.     

Mitigating Interest Rate Risk in Variable Annuities: An Analysis of Hedging Effectiveness under Model Risk

Variable annuities are investment vehicles offered by insurance companies that combine a life insurance policy with long-term financial guarantees. These guarantees expose the insurer to market risks, such as volatility and interest rate risks, which can be managed only with a hedging strategy. The objective of this article is to study the effectiveness of dynamic delta-rho hedging strategies for mitigating interest rate risk in variable annuities with either a guaranteed minimum death benefit or guaranteed minimum withdrawal benefit rider. Our analysis centers on three important practical issues: (1) the robustness of delta-rho hedging strategies to model uncertainty, (2) the impact of guarantee features (maturity versus withdrawal benefits) on the performance of the hedging strategy, and (3) the importance of hedging interest rate risk in either a low and stable or rising interest rate environment. Overall, we find that the impact of interest rate risk is equally felt for the two types of products considered, and that interest rate hedges do lead to a significant risk reduction for the insurer, even when the ongoing low interest rate environment is factored in.     

The Poisson Log-Bilinear Lee-Carter Model

Abstract

Life insurance companies deal with two fundamental types of risks when issuing annuity contracts: financial risk and demographic risk. Recent work on the latter has focused on modeling the trend in mortality as a stochastic process. A popular method for modeling death rates is the Lee-Carter model. This methodology has become widely used, and various extensions and modifications have been proposed to obtain a broader interpretation and to capture the main features of the dynamics of mortality rates. In order to improve the measurement of uncertainty in survival probability estimates, in particular for older ages, the paper proposes an extension based on simulation procedures and on the bootstrap methodology. It aims to obtain more reliable and accurate mortality projections, based on the idea of obtaining an acceptable accuracy of the estimate by means of variance reducing techniques. In this way the forecasting procedure becomes more efficient. The longevity question constitutes a critical element in the solvency appraisal of pension annuities. The demographic models used for the cash flow distributions in a portfolio impact on the mathematical reserve and surplus calculations and affect the risk management choices for a pension plan. The paper extends the investigation of the impact of survival uncertainty for life annuity portfolios and for a guaranteed annuity option in the case where interest rates are stochastic. In a framework in which insurance companies need to use internal models for risk management purposes and for determining their solvency capital requirement, the authors consider the surplus value, calculated as the ratio between the market value of the projected assets to that of the liabilities, as a meaningful measure of the company’s financial position, expressing the degree to which the liabilities are covered by the assets.     

Produktgarantien und Aktienkrise — Implikationen für die Kapitalanlagepolitik von Lebensversicherungsunternehmen

The present contribution analyzes the implications of two central factors influencing the asset allocation decision of (German) life insurance companies, the development of the equity market on one hand and the interest rate guarantees included in traditional life insurance products on the other. The adverse development of share prices in 2000–2002 implies the necessity to consider not only ?normal“ volatility but also worst case-developments for the purpose of risk control. Formally this is done by using the risk measures value-at-risk and conditional value-at-risk. The specific ?myopic“ nature of interest rate guarantees in German life insurance products, which are granted on a yearly basis implies — beyond the general control of the shortfall risk with respect to the guaranteed interest rates — the necessity to per-form the asset allocation on a yearly basis to be in conformity with the time horizon of the liabilities.On the basis of a quantitative approach corresponding model calculations are performed. Thereby not only a pure market valuation is considered but also institutional peculiarities (hidden reserves, accounting norms) of German life insurance companies. The possibility of a riskless one-year investment, either based on market values or on balance sheet values, is revealed to be crucial for giving interest rate guarantees on a yearly basis.     

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.     

What do asset prices have to say about risk appetite and uncertainty?

Building on intuition from the dynamic asset pricing literature, we uncover unobserved risk aversion and fundamental uncertainty from the observed time series of the variance premium and the credit spread while controlling for the conditional variance of stock returns, expectations about the macroeconomic outlook, and interest rates. We apply this methodology to monthly data from both Germany and the US. We find that the variance premium contains a substantial amount of information about risk aversion whereas the credit spread has a lot to say about uncertainty. We link our risk aversion and uncertainty estimates to practitioner and “academic” risk aversion indices, sentiment indices, financial stress indices, business cycle indicators and liquidity measures.     

Background Risk, Demand for Insurance, and Choquet Expected Utility Preferences

This article deals with demand for insurance with a background risk in a nonprobabilized uncertainty framework, where preferences are represented by a nonadditive model of decision making. The Choquet expected utility model that we use generalizes expected utility and allows for a separation of the attitude towards uncertainty and the attitude towards wealth. When the insurable and the background risk are comonotone, the impact of the background risk on the demand for insurance is related to the attitude towards wealth. In contrast, when the two risks are anticomonotone, the attitude towards uncertainty is determinant. In this case, some of the resulting behaviors cannot be explained by the standard expected utility model.     

Macroeconomic risk and hedge fund returns

This paper estimates hedge fund and mutual fund exposure to newly proposed measures of macroeconomic risk that are interpreted as measures of economic uncertainty. We find that the resulting uncertainty betas explain a significant proportion of the cross-sectional dispersion in hedge fund returns. However, the same is not true for mutual funds, for which there is no significant relationship. After controlling for a large set of fund characteristics and risk factors, the positive relation between uncertainty betas and future hedge fund returns remains economically and statistically significant. Hence, we argue that macroeconomic risk is a powerful determinant of cross-sectional differences in hedge fund returns.     

Cohort and value-based multi-country longevity risk management

ABSTRACT

Multi-country risk management of longevity risk provides new opportunities to hedge mortality and interest rate risks in guaranteed lifetime income streams. This requires consideration of both interest rate and mortality risks in multiple countries. For this purpose, we develop value-based longevity indexes for multiple cohorts in two different countries that take into account the major sources of risks impacting life insurance portfolios, mortality and interest rates. To construct the indexes we propose a cohort-based affine model for multi-country mortality and use an arbitrage-free multi-country Nelson–Siegel model for the dynamics of interest rates. Index-based longevity hedging strategies have the advantages of efficiency, liquidity and lower cost but introduce basis risk. Graphical risk metrics are a way to effectively capture the relationship between an insurer's portfolio and hedging strategies. We illustrate the effectiveness of using a value-based index for longevity risk management between two countries using graphical basis risk metrics. To show the impact of both interest rate and mortality risk we use Australia and the UK as domestic and foreign countries, and, to show the impact of mortality only, we use the male populations of the Netherlands and France with common interest rates and basis risk arising only from differences in mortality risks.     

论模糊风险树分析方法在我国保险综合经营风险控制中的应用

本文针对保险综合经营中风险结构复杂,风险传递等发生概率具有模糊性和不确定性的特点,运用模糊风险树的方法绘制出保险综合经营系统风险树,由此探索保险综合经营风险的形成机理,制定全面风险管理的制度、流程和预控方法。