Compound gamma bivariate distributions

Summary Bivariate distributions, which may be of special relevance to the lifetimes of two components of a system, are derived using the following approach. As the two components are part of one system and therefore exposed to similar conditions of service, there will be similarity between their lifetimes that is not shared by components belonging to different systems. The lifetime distribution for a given system is assumed to be Gamma in form (this includes the exponential as a special case; extension to the Stacey distribution, which includes the Weibull distribution, is straightforward). The scale parameter of this distribution is itself a random variable, with a Gamma distribution. We thus obtain what might be termed a compound Gamma-Gamma bivariate distribution. The cumulative distribution function of this may be expressed in terms of one of the double hypergeometric functions of Appell.Generalised hypergeometric functions play an important part in this paper, and one of Saran's triple hypergeometric functions is obtained when generalising the above model to permit the scale parameters of the distributions for the two components to be correlated, rather than identical.Work started while the author was with the Transport Studies Group, University College London.     

The relationships among professional competence,job satisfaction and career development confidence for chefs in Taiwan

This study explores the relationship among professional competence, job satisfaction and the career development confidence for chefs, and examines the mediators of job satisfaction for professional competence and career development confidence in Taiwan. The analytical results demonstrate that work attitude was the most influential construct for professional competence, and culinary creativity had the lowest reported ratings. Job selection satisfaction showed higher ranking than current job satisfaction. The structural equation modeling results showed that professional competence significantly affects job satisfaction, and that job satisfaction predicts actual career development confidence. Additionally, job satisfaction mediated the influences of professional competence and career development confidence. The implications of these findings are discussed.     

Improving on two-stage estimators for scale families

Summary Consider the problem of finding an estimator for a scale parameter such that its risk function is bounded by a preassigned constant. As a solution of the problem, two-stage estimators based on only the second sample have been proposed. The paper shows that these estimators can be improved by combining the first and the second sample.     

A Simple Model of Insurance Market Dynamics

Abstract

This paper constructs and studies a simple but realistic model of an insurance market. The model has a minimalist construction in the sense that the number of parameters defining it is strictly limited and the elimination of any one of them would destroy its realism. There are 11 essential parameters. Each of the parameters has a physical interpretation. Some determine competitive effects within the market, some barriers to entry, and so on. The effect of each on various aspects of the market is examined in the presence of simulated loss experience. The aspects of the market considered include stability of premium rates, profitability, and market concentration. Some of the parameters are capable of use as regulatory controls. Two parameters, in addition to the original 11, are explicit price controls. Despite its simplicity, the model displays considerably complex behavior. Some results are intuitive, but some are not. For this reason, regulatory controls need to be applied with great caution lest they induce perverse effects, possibly even the reverse of those intended. The effect of the parameters on market behavior is first studied in the absence of catastrophic events from the loss experience. Subsequently, the effect of a single such event is studied.     

Pricing Annuity Guarantees Under a Regime-Switching Model

Abstract

We consider the pricing problem of equity-linked annuities and variable annuities under a regimeswitching model when the dynamic of the market value of a reference asset is driven by a generalized geometric Brownian motion model with regime switching. In particular, we assume that regime switching over time according to a continuous-time Markov chain with a finite number state space representing economy states. We use the Esscher transform to determine an equivalent martingale measure for fair valuation in the incomplete market setting. The paper is complemented with some numerical examples to highlight the implications of our model on pricing these guarantees.     

Multiperiod Optimal Investment-Consumption Strategies with Mortality Risk and Environment Uncertainty

Abstract

In this article we investigate three related investment-consumption problems for a risk-averse investor: (1) an investment-only problem that involves utility from only terminal wealth, (2) an investment-consumption problem that involves utility from only consumption, and (3) an extended investment-consumption problem that involves utility from both consumption and terminal wealth. Although these problems have been studied quite extensively in continuous-time frameworks, we focus on discrete time. Our contributions are (1) to model these investmentconsumption problems using a discrete model that incorporates the environment risk and mortality risk, in addition to the market risk that is typically considered, and (2) to derive explicit expressions of the optimal investment-consumption strategies to these modeled problems. Furthermore, economic implications of our results are presented. It is reassuring that many of our findings are consistent with the well-known results from the continuous-time models, even though our models have the additional features of modeling the environment uncertainty and the uncertain exit time.