Actuarial validity of the binomial distribution for large numbers of lives with small mortality probabilities

Abstract

In a previous paper (see reference [1]), the binomial distribution was shown to be valid under rather general conditions for the case of a large number of statistically independent lives with possibly unequal mortality probabilities. This note extends these results to some situations where the lives are not necessarily statistically independent. An analysis is presented which indicates that these situations include most actuarial applications involving a large number of lives.     

The mortality among industrial insured lives in Norway during the war

In the Norwegian life insurance company Fram a continuous mortality investigation takes place in connection with the yearly valuation of policies issued with weekly premiums. The investigation gives the aggregate mortality, the unit is the policy and the year of observation is the calendar year. A detailed account of the method used has been given by Fredrik Borch in his paper: “The mortality among industrial insured lives in Norway 1931–1940” in this journal 1943. The most important results of the investigation from the years 1940–1946 are rendered below.     

Duality and convergence for binomial markets with friction

We prove limit theorems for the super-replication cost of European options in a binomial model with friction. Examples covered are markets with proportional transaction costs and illiquid markets. A dual representation for the super-replication cost in these models is obtained and used to prove the limit theorems. In particular, the existence of a liquidity premium for the continuous-time limit of the model proposed in Çetin et al. (Finance Stoch. 8:311–341, 2004) is proved. Hence, this paper extends the previous convergence result of Gökay and Soner (Math Finance 22:250–276, 2012) to the general non-Markovian case. Moreover, the special case of small transaction costs yields, in the continuous limit, the G-expectation of Peng as earlier proved by Kusuoka (Ann. Appl. Probab. 5:198–221, 1995).     

Are incentives for earnings management reflected in the ERC: Large sample evidence

In this study, I examine the effect of exposure to earnings management (EM) incentives on the earnings response coefficient (ERC). Drawing from several anecdotes and normative arguments about the implications of managers' incentives for investor perception, I predict and test that exposure to EM incentives is negatively associated with the ERC. I find that ERC is reliably lower for firms with elevated exposure to EM incentives, holding constant the effects of actual EM and other factors that affect the returns–earnings relation. Furthermore, the effect of the incentive exposure on cash flows as well as on total accruals is reliably negative. These results are robust across alternative price– and returns–earnings specifications, and are insensitive to the inclusion of other measures of earnings quality. Additional analysis shows that the effect of such incentives on the ERC is more pronounced at higher levels of institutional stock ownership. However, a certain class of institutional owners – transient institutions – are less sensitive to the implications of such incentives for earnings quality.     

On the validity of accounting rates of return in cross-sectional analysis: Theory, evidence, and implications

This paper reports the results of an empirical examination of the relationship between firm accounting rate of return (ARR) and firm internal rate of return (IRR). The evidence presented shows that some of the analytically derived properties of the ARR-IRR relationship hold in a sample of U.S. manufacturing firms. This evidence can be interpreted as documenting the existence of a potentially important degree of measurement error in the ARR for a sample of actual firms and increases the credibility of those who have questioned the use of accounting rates of return as the dependent variable in cross-sectional studies of firm profitability.     

On the optimum spacing of sample quantiles from a normal distribution. Part I

Abstract

Assume that a large number of observations are made on a normal random variable with the density function where σ σ 0, When the sample is very large the ordinary estimates of µ and a involve considerable computational work. In order to simplify the estimation of µ and/or σ it is sometimes convenient to select a small number of sample quantiles and to use estimates which are linear functions of these sample quantiles, Such a procedure is particularly convenient when the observations occur naturally in order of magnitude, which happens in life testing, for instance, Let      

Comparison of body mass index and waist circumference as predictors of all-cause mortality in a male insured lives population

Obesity assessed by body mass index (BMI) is associated with increased mortality risk, but there is uncertainty about whether BMI is the best way to measure obesity. Waist circumference (WC) has been proposed as a better measure. The Swiss Re BMI/WC Study was conducted to determine whether BMI or WC is a better predictor of future all-cause mortality in a large male insurance population. Using Cox proportional hazard models, risk ratios for increasing BMI and WC were 1.033 (P < .001) and 1.027 (P < .001), respectively. Risk ratios for obesity defined by BMI > or = 30 kg/m2 and WC > or = 40 inches were 1.33 (P < .001) and 1.20 (P = .002), respectively. In this study, BMI and WC are essentially equivalent in their ability to predict mortality risk in a male insurance population. Obesity, measured by either BMI or WC, has important underwriting and pricing implications.     

On the consequences of demographic change for rates of returns to capital, and the distribution of wealth and welfare

This paper employs a multi-country large-scale Overlapping Generations model with uninsurable labor productivity and mortality risk to quantify the impact of the demographic transition towards an older population in industrialized countries on world-wide rates of return, international capital flows and the distribution of wealth and welfare in the OECD. We find that for the U.S. as an open economy, rates of return are predicted to decline by 86 basis points between 2005 and 2080 and wages increase by about 4.1%. If the U.S. were a closed economy, rates of return would decline and wages increase by less. This is due to the fact that other regions in the OECD will age even more rapidly; therefore the U.S. is “importing” the more severe demographic transition from the rest of the OECD in the form of larger factor price changes. In terms of welfare, our model suggests that young agents with little assets and currently low labor productivity gain, up to 1% in consumption, from higher wages associated with population aging. Older, asset-rich households tend to lose, because of the predicted decline in real returns to capital.     

Get inside the lives of your customers

Many companies have become adept at the art of customer relationship management. They've collected mountains of data on preferences and behavior, divided buyers into ever-finer segments, and refined their products, services, and marketing pitches. But all too often those efforts are too narrow--they concentrate only on the points where the customer comes into contact with the company. Few businesses have bothered to look at what the author calls the customer scenario--the broad context in which customers select, buy, and use products and services. As a result, consultant Patricia Seybold maintains, they've routinely missed chances to deepen loyalty and expand sales. In this article, the author shows how effective three very different companies have been at using customer scenarios as the centerpiece of their marketing plans. Chip maker National Semiconductor looked beyond the purchasing agents that buy in bulk to find ways to make it easier for engineers to design National's components into their specifications for mobile telephones. Each time they do so, it translates into millions of dollars in orders. By developing a customer scenario that describes how people actually shop for groceries, Tesco learned the importance of decentralizing its Web shopping site and how the extra costs of decentralization could be outweighed by the higher profit margins on-line customers generate. And Buzzsaw.com used customer scenarios as the basis for its entire business. It has used the Web to create a better way for the dozens of participants in a construction project to share their drawings and manage their projects. Seybold lays out the steps managers can take to develop their own customer scenarios. By thinking broadly about the challenges your customers face, she suggests, you can almost always find ways to make their lives easier--and thus earn their loyalty.     

Targeting public services through the unequal treatment of unequals

When private goods are publicly provided, government authorities have to determine the distribution of in-kind benefits to recipients. In this paper, the public service provider is assumed to maximize utility defined over public service supply to different target groups, given a budget constraint. The production technology is target-group-specific and depends on the ability of each target group to produce service outcomes. Three benchmark allocation principles are identified: equality of treatment (ET), equality of outcome (EO), and equality of marginal cost (EMC). These principles can be considered to be consistent with special cases of a public preference model, which allows for compromises between different allocation principles. The condition of technological dominance implies that there is a clear-cut equity–productivity trade-off, whereas violations of this condition may reduce the significance of the trade-off.     

A note on the efficiency of the binomial option pricing model

We discuss the efficiency of the binomial option pricing model for single and multivariate American style options. We demonstrate how the efficiency of lattice techniques such as the binomial model can be analysed in terms of their computational cost. For the case of a single underlying asset the most efficient implementation is the extrapolated jump-back method: that is, to value a series of options with nested discrete sets of early exercise opportunities by jumping across the lattice between the early exercise times and then extrapolating from these values to the limit of a continuous exercise opportunity set. For the multivariate case, the most efficient method depends on the computational cost of the early exercise test. However, for typical problems, the most efficient method is the standard step-back method: that is, performing the early exercise test at each time step.     

Derivation of the Wishart distribution of the second order sample moments by straightforward integration of a multiple integral

1. Introduction.

In his textbook of statistics Kendall classifies the methods of deducing exact sampling distributions into four groups:

• (a) straightforward evaluation of the integral in question by ordinary analytical processes such as a convenient change of variable;

• (b) the use of geometrical terminology;

• (c) the use of characteristic functions; and

• (d) other analytical methods.

     

Assessing the validity of the Delphi technique

Forecasting is an essential factor in policy formulation and planning. It helps determine the direction of future actions. While a number of forecasting techniques are utilized to forecast the future, it is important to know just how valid those forecasting techniques can be. The Delphi technique has been called the ‘cornerstone of futures research’. This study reports the results of the assessment of the accuracy of the forecasts derived from the Delphi technique. Twenty-five experts in the communication field assessed 24 trends and 17 events in the state of Hawaii as of 1991. The expert assessments were then compared with the forecasts made by utilizing the Delphi technique 16 years earlier. The results showed that the trend forecasts were significantly correlated with the trend assessment. They also showed that the Delphi technique had accurately forecast approximately half the events that could be evaluated as of 1991. Results from this study lend support to the use of the Delphi technique in long-range forecasting and reveal some interesting findings in forecasting the developments in communication in Hawaii.     

Arbitrage bounds for the term structure of interest rates

This paper proposes a methodology for simultaneously computing a smooth estimator of the term structure of interest rates and economically justified bounds for it. It unifies existing estimation procedures that apply regression, smoothing and linear programming methods. Our methodology adjusts for possibly asymmetric transaction costs. Various regression and smoothing techniques have been suggested for estimating the term structure. They focus on what functional form to choose or which measure of smoothness to maximize, mostly neglecting the discussion of the appropriate measure of fit. Arbitrage theory provides insight into how small the pricing error will be and in which sense, depending on the structure of transaction costs. We prove a general result relating the minimal pricing error one incurs in pricing all bonds with one term structure to the maximal arbitrage profit one can achieve with restricted portfolios.     

降低信用卡透支利率和透支利率市场化改革探析

信用卡业务作为金融业的一项新兴业务,正以迅猛之势在国内发展.在为公众提供"无担保、无抵押、无指定用途的个人小额消费信贷服务"的同时,信用卡业务也为促进消费、拉动内需做出了积极的贡献.