“Analysis of Incremental Returns of Canadian Mutual Funds”, J. F. Carrière; C. F. Hill,April 2001

Abstract

The determination and allocation of economic capital is important for pricing, risk management, and related insurer financial decision making. This paper considers the allocation of economic capital to lines of business in insurance. We show how to derive closed-form results for the complete markets, arbitrage-free allocation of the insurer default option value, or insolvency exchange option, to lines of business for an insurer balance sheet. We assume that individual lines of business and the surplus ratio are joint log-normal although the method we adopt allows other assumptions. The allocation of the default option value is required for fair pricing in the multiline insurer. We discuss and illustrate other methods of capital allocation, including Myers-Read, and give numerical examples for the capital allocation of the default option value based on explicit payoffs by line.     

Valuation portfolio in non-life insurance

The purpose of this paper is the construction of the Valuation Portfolio (VaPo) for a non-life insurance company. The VaPo represents the obligations of the insurer for the whole period of his insurance contracts. These obligations are not simply measured by a one-dimensional figure (as standard for reserves in practice), but are expressed as a portfolio of financial instruments. Hence, the actuarial reserves become multidimensional. The financial instruments in the VaPo are a properly chosen basis to represent the future cashflows resulting from the insurance contracts.

In this setup, financial and technical risks are clearly separated. The financial fluctuations derive from the basis elements, the technical fluctuations are covered by an increased number of basis elements (VaPo protected against technical risks). We show how this protection can be calculated in the case of a non-life insurance company.     

The Effects of Customer Satisfaction on Company Profitability: Evidence From the Property and Casualty Insurance Industry

Prior literature presents a positive link between customer satisfaction and firms’ financial outcomes, including greater revenue, profitability, and prices. However, few studies approach the topic of customer satisfaction in the insurance industry. Using a unique data set obtained from J.D. Power, we observe customer satisfaction among U.S. auto insurers and link their customer satisfaction rating to insurer profitability metrics. Our results support the notion that greater customer satisfaction leads to reduced expenses and increased profitability. A potential explanation is that more satisfied customers are more likely to remain with an insurance company and refer others to the insurer, reducing customer acquisition expenses.     

Wer trägt das Terrorrisiko?

This article deals with insuring terrorism risks and it focuses on the situation in Germany after the events of September 11^th 2001. After a brief introduction to the general problems of insuring against terrorism the authors explore how terrorism affects different lines of insurance business in Germany and examine Extremus, the German specialist insurer with government backing for insuring property risks against terrorism. A thorough analysis of different aspects of risk transfer follows. This analysis also addresses different pricing strategies for insuring against terrorism. In this section the authors focus on the question to what extend one can really speak of a risk transfer through insurance in respect to terrorism. Scenarios are developed of how large losses would affect the insurance industry as well as the customers. In regard to those scenarios it becomes visible that the risk transfer from the policyholder to the insurer is not complete.In their conclusion the authors examine some scenarios of increased and decreased terrorist activity and the effects that each of these scenarios will have on the solution of insuring against terrorism through Extremus.     

Interplay of insurance and financial risks in a stochastic environment

Consider an insurer who makes risky investments and hence faces both insurance and financial risks. The insurance business is described by a discrete-time risk model modulated by a stochastic environment that poses systemic and systematic impacts on both the insurance and financial markets. This paper endeavors to quantitatively understand the interplay of the two risks in causing ruin of the insurer. Under the bivariate regular variation framework, we obtain an asymptotic formula to describe the impacts on the insurer's solvency of the two risks and of the stochastic environment.     

Überlegungen zu einem fairen Risikomanagement-Mix in Versicherungsunternehmen

This article deals with the question of how a ?fair risk management mix“ that does not lead to a wealth transfer between shareholders and policyholders can be achieved in a joint-stock insurance company. In our financial model of an insurer, the ?fair“ situation, it is assumed that there is no wealth transfer between shareholders and policyholders when both parties receive a net present value of zero on their investments. Taking the default risk of the insurance company into account, we first model a ?fair“ situation for the insurer’s existing portfolio. Surprisingly, closing a new insurance contract that has been priced on a fair basis and then included in the insurer’s existing portfolio leads to a disequilibrium situation because the net present value for the shareholders is no longer zero. This new net present value can be viewed as the fair price of any risk management measure the insurer must take so as to reestablish an equilibrium for both parties, the shareholders and the policyholders.     

后危机时代保险公司盈利模式选择的理论分析

全球金融危机的冲击下促使人们重新思考保险公司未来的盈利模式选择。保险产品是风险转移和服务业务的有机组合。后金融危机时代中国保险公司盈利模式的＂回归＂并不是回到单一的保险模式,而是要改变＂过分强调投资模式而服务模式发展滞后＂的不合理的业务结构。因此,在坚持保险模式为本的基础上,以＂服务模式＂的提升作为当前中国保险公司盈利模式改进的突破点,切实转变保险业的发展方式;根据经济社会环境的发展变化均衡保险模式、服务模式和投资模式的资源配置和盈利贡献,形成保险公司动态的组合盈利模式,以保证中国保险业的全面协调可持续发展。     

Risk assessment of surplus appropriation schemes in participating life insurance

The aim of this paper is to analyze a life insurance company’s risk exposure with respect to different surplus appropriation schemes in participating life insurance. In this regard, three surplus appropriation schemes are considered, including the bonus system, the interest-bearing accumulation, and the system of shortening the contract term. We further examine an insurance company that offers all three schemes, i.e. each system is used for one third of the policyholders. Focus is laid on the effect of different asset portfolios and shocks to mortality on the insurer’s risk situation with respect to the policyholder’s age level at contract inception.     

Time-consistent mean-variance reinsurance-investment strategy for insurers under CEV model

We consider an optimal time-consistent reinsurance-investment strategy selection problem for an insurer whose surplus is governed by a compound Poisson risk model. In our model, the insurer transfers part of the risk due to insurance claims via a proportional reinsurance and invests the surplus in a simplified financial market consisting of a risk-free asset and a risky stock. The dynamics of the risky stock is governed by a constant elasticity of variance model to incorporate conditional heteroscedasticity as well as the feedback effect of an asset’s price on its volatility. The objective of the insurer is to choose an optimal time-consistent reinsurance-investment strategy so as to maximize the expected terminal surplus while minimizing the variance of the terminal surplus. We investigate the problem using the Hamilton-Jacobi-Bellman dynamic programming approach. Closed-form solutions for the optimal reinsurance-investment strategies and the corresponding value functions are obtained in both the compound Poisson risk model and its diffusion approximation. Numerical examples are also provided to illustrate how the optimal reinsurance-investment strategy changes when some model parameters vary.     

Bank health in varying macroeconomic conditions: A panel study

Using panel data on selected Financial Soundness Indicators (FSIs) this paper investigates the potential strengths and vulnerabilities of financial intermediaries across more than 50 countries. Our econometric analysis reveals strong influence of business cycle, inflation, and real effective exchange rates, and size of the industry on capital adequacy —a core indicator of banks' financial soundness. Furthermore, our analyses provide evidence that banks' profitability is determined by a combination of macroeconomic, bank specific and industry characteristics such as business cycle, inflation, credit risk, capital adequacy, and the level of competition.     

The Use of Dynamic Financial Analysis to Determine Whether an Optimal Growth Rate Exists for a Property-Liability Insurer

Prior research on the aging phenomenon has demonstrated that new business for property‐liability (P‐L) insurers generates high loss ratios that gradually decline as a book of business goes through successive renewal cycles. Although the experience on new business is initially unprofitable, the renewal book of business eventually becomes profitable over time. Within this context, insurers need to manage their exposure growth in order to maximize long run profitability. Dynamic financial analysis (DFA), a relatively new tool for P‐L insurers, utilizes Monte Carlo simulation to generate the overall financial results for an insurer under a large number of scenarios. This article uses a publicly available DFA model—along with the estimated market value of an insurer, based on 1990–2001 data for stock P‐L insurers and underlying financial variables—to determine optimal growth rates of a P‐L insurer based on mean–variance analysis, stochastic dominance, and constraints on leverage.     

Optimal Reinsurance and Investment for a Jump Diffusion Risk Process under the CEV Model

Abstract

We consider an optimal reinsurance-investment problem of an insurer whose surplus process follows a jump-diffusion model. In our model the insurer transfers part of the risk due to insurance claims via a proportional reinsurance and invests the surplus in a “simplified” financial market consisting of a risk-free asset and a risky asset. The dynamics of the risky asset are governed by a constant elasticity of variance model to incorporate conditional heteroscedasticity. The objective of the insurer is to choose an optimal reinsurance-investment strategy so as to maximize the expected exponential utility of terminal wealth. We investigate the problem using the Hamilton-Jacobi-Bellman dynamic programming approach. Explicit forms for the optimal reinsuranceinvestment strategy and the corresponding value function are obtained. Numerical examples are provided to illustrate how the optimal investment-reinsurance policy changes when the model parameters vary.     

Solvency, Capital Allocation, and Fair Rate of Return in Insurance

In this article, we consider the links between solvency, capital allocation, and fair rate of return in insurance. A method to allocate capital in insurance to lines of business is developed based on an economic definition of solvency and the market value of the insurer balance sheet. Solvency, and its financial impact, is determined by the value of the insolvency exchange option. The allocation of capital is determined using a complete markets’ arbitrage‐free model and, as a result, has desirable properties, such as the allocated capital “adds up” and is consistent with the economic value of the balance sheet assets and liabilities. A single‐period discrete‐state model example is used to illustrate the results. The impact of adding lines of business is briefly considered.     

Wertorientierte Kapitalanlagestrategie eines als Kapitalgesellschaft verfassten Versicherungsunternehmens

The question, inasmuch the allocation of shareholder capital to support capital market risks of an insurance company is value-accreditive is not only a very timely issue for market-affine shareholders given the current state of the financial markets, recent changes of insurance contract act, and an increasingly risk-adequate regulation. Moreover, the questions at hand touches upon very fundamental aspects of the risk/return business model of an insurance company. Applying established mirco- and institutional-economic concepts the analysis fundamentally denies such a value-contribution from a shareholder point of view. Yet, both for non-life- as well as in particular life-operations exceptions to this rule are also explored.     

Optimal asset allocation for participating contracts under the VaR and PI constraint

ABSTRACT

Participating contracts provide a maturity guarantee for the policyholder. However, the terminal payoff to the policyholder should be related to financial risks of participating insurance contracts. We investigate an optimal investment problem under a joint value-at-risk and portfolio insurance constraint faced by the insurer who offers participating contracts. The insurer aims to maximize the expected utility of the terminal payoff to the insurer. We adopt a concavification technique and a Lagrange dual method to solve the problem and derive the representations of the optimal wealth process and trading strategies. We also carry out some numerical analysis to show how the joint value-at-risk and the portfolio insurance constraint impacts the optimal terminal wealth.     

To Hedge or Not to Hedge: Managing Demographic Risk in Life Insurance Companies

Demographic risk, i.e., the risk that life tables change in a nondeterministic way, is a serious threat to the financial stability of an insurance company having underwritten life insurance and annuity business. The inverse influence of changes in mortality laws on the market value of life insurance and annuity liabilities creates natural hedging opportunities. Within a realistically calibrated shareholder value (SHV) maximization framework, we analyze the implications of demographic risk on the optimal risk management mix (equity capital, asset allocation, and product policy) for a limited liability insurance company operating in a market with insolvency‐averse insurance buyers. Our results show that the utilization of natural hedging is optimal only if equity is scarce. Otherwise, hedging can even destroy SHV. A sensitivity analysis shows that a misspecification of demographic risk has severe consequences for both the insurer and the insured. This result highlights the importance of further research in the field of demographic risk.     

Macroeconomic influences on optimal asset allocation

We develop a tactical asset allocation strategy that incorporates the effects of macroeconomic variables. The joint distribution of financial asset returns and the macroeconomic variables is modelled using a VAR with a multivariate GARCH (M-GARCH) error structure. As a result, the portfolio frontier is time varying and subject to contagion from the macroeconomic variable. Optimal asset allocation requires that this be taken into account. We illustrate how to do this using three risky UK assets and inflation as a macroeconomic factor. Taking account of inflation generates portfolio frontiers that lie closer to the origin and offers investors superior risk-return combinations.     

Empirical Evidence on the Value of Group‐Level Financial Information in Insurer Solvency Surveillance

The existing empirical research on insurer insolvency relies almost exclusively upon individual insurance company financial data, even though the insurance industry is dominated by group‐affiliated firms. This is the first study to evaluate the benefit of using group‐level data to predict insurer insolvencies for group‐affiliated insurers. The study uses financial ratios from the NAIC FAST scoring system, measured at both the company level and group level, as potential predictor variables. The results indicate that group‐level financial information substantially improves the predictive power of an insolvency prediction model relative to a model that uses only the analogous company‐level variables. In fact, the group‐level variables are found to often be substantially more powerful than company‐level variables in predicting individual insurer insolvencies. These results suggest that future insolvency analysis should, whenever feasible, include group‐level information to obtain higher predictive accuracy.     

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.     

Sarmanov Family of Bivariate Distributions for Multivariate Loss Reserving Analysis

The correlation among multiple lines of business plays a critical role in aggregating claims and thus determining loss reserves for an insurance portfolio. We show that the Sarmanov family of bivariate distributions is a convenient choice to capture the dependencies introduced by various sources, including the common calendar year, accident year, and development period effects. The density of the bivariate Sarmanov distributions with different marginals can be expressed as a linear combination of products of independent marginal densities. This pseudo-conjugate property greatly reduces the complexity of posterior computations. In a case study, we analyze an insurance portfolio of personal and commercial auto lines from a major U.S. property-casualty insurer.