Increasing failure rate and decreasing reversed hazard rate properties of the minimum and maximum of multivariate distributions with log-concave densities

For a multivariate random vector X = (X ₁,...,X _n ) with a log-concave density function, it is shown that the minimum min{X ₁,...,X _n } has an increasing failure rate, and the maximum max{X ₁,...,X _n } has a decreasing reversed hazard rate. As an immediate consequence, the result of Gupta and Gupta (in Metrika 53:39–49, 2001) on the multivariate normal distribution is obtained. One error in Gupta and Gupta method is also pointed out.      

Stochastic comparisons of multivariate reversed frailty model

Multivariate frailty approaches are most commonly used to define distributions of random vectors, which represent lifetimes of individuals or components and stochastically compare them in terms of various multivariate orders. In this paper, we study a multivariate shared reversed frailty model and a general multivariate reversed frailty mixture model, and derive sufficient conditions for some of the stochastic orderings to hold among the random vectors. We also consider a particular case of a general multivariate mixture model in which the baseline distribution function is represented in terms of a copula and study stochastic comparisons (stochastic and lower orthant order) among the two random vectors.     

Estimation in Varying-coefficient Proportional Hazard Regression Model

In this paper, varying coefficient proportional hazard regression models are considered. The model is an important extension of the Cox model, and arises naturally if the coefficients change over different groups characterized by certain covariates in practice. Under random censorship, weighted partial likelihood estimators are defined for the varying coefficients by maximizing weighted partial likelihoods. It is shown that the proposed estimators are consistent and asymptotically normal.     

Monotonicity of the (reversed) hazard rate of the (maximum) minimum in bivariate distributions

It is well known that in the case of independent random variables, the (reversed) hazard rate of the (maximum) minimum of two random variables is the sum of the individual (reversed) hazard rates and hence the onotonicity of the (reversed) hazard rate of the marginals is preserved by the monotonicity of the (reversed) hazard rate of the (maximum) minimum. However, for the bivariate distributions this property is not always preserved. In this paper, we study the monotonicity of the (reversed) hazard rate of the (maximum) minimum for two well known families of bivariate distributions viz the Farlie-Gumbel-Morgenstern (FGM) and Sarmanov family. In case of the FGM family, we obtain the (reversed) hazard rate of the (maximum) minimum and provide several examples in some of which the (reversed) hazard rate is monotonic and in others it is non-monotonic. In the case of Sarmanov family the (reversed) hazard rate of the (maximum) minimum may not be expressed in a compact form in general. We consider some examples to illustrate the procedureResearch of the second author is supported by a grant from Natural Sciences and Engineering Research Council and the research of the other two authors is partially supported by a travel grant from the Canadian American Center of the University of Maine     

On the discrete mean past lifetime

Let T denote a positive discrete survival time and n a non-negative integer number. Properties of the mean past lifetime E(n  −  T|T  <  n) are provided. M. Asadi’s work is supported by the University of Isfahan Grant 850713.     

Some Properties of Past Entropy and their Applications

In the context of information theory, measure of uncertainty in past lifetime distribution has been proposed by Di Crescenzo and Longobardi (J Appl Probab 39:434–440, 2002). In this paper, we study some ordering and aging properties in terms of past entropy (based on past lifetime) and develop some characterization results. Some discrete distribution results are also addressed here.     

On moral hazard and nonexclusive contracts

We study an economy where intermediaries compete over contracts in a nonexclusive insurance market affected by moral hazard. In this context, we show that, contrarily to what is commonly believed, market equilibria may fail to be efficient even if the planner is not allowed to enforce exclusivity of trades (third best inefficiency). Our setting is the same as that of Bisin and Guaitoli [Bisin, A., Guaitoli, D., 2004. Moral hazard with nonexclusive contracts. Rand Journal of Economics 2, 306–328]. We hence argue that some of the equilibrium conditions they imposed are not necessary, and we exhibit a set of equilibrium allocations which fail to satisfy them.     

Ordering results of the smallest and largest order statistics from independent heterogeneous exponentiated gamma random variables

In this paper, we discuss stochastic comparisons of lifetimes of series and parallel systems with heterogeneous exponentiated gamma components. The results established here are developed in two directions. First, when a system possibly has different shape and scale parameters and the matrix of those different parameters following the chain majorization order, we study the reversed hazard rate order of parallel systems and the usual stochastic order of series systems. Next, by using the concept of vector majorization, we establish the usual stochastic order of series systems and the reversed hazard rate order of parallel systems.     

Smooth estimation of a monotone hazard and a monotone density under random censoring

We consider kernel smoothed Grenander‐type estimators for a monotone hazard rate and a monotone density in the presence of randomly right censored data. We show that they converge at rate n^2/5 and that the limit distribution at a fixed point is Gaussian with explicitly given mean and variance. It is well known that standard kernel smoothing leads to inconsistency problems at the boundary points. It turns out that, also by using a boundary correction, we can only establish uniform consistency on intervals that stay away from the end point of the support (although we can go arbitrarily close to the right boundary).     

Repeated moral hazard and recursive Lagrangeans

This paper shows how to solve dynamic agency models by extending recursive Lagrangean techniques à la Marcet and Marimon (2011) to problems with hidden actions. The method has many advantages with respect to the promised utilities approach (Abreu et al., 1990): it is a significant improvement in terms of simplicity, tractability and computational speed. Solutions can be easily computed for hidden actions models with several endogenous state variables and several agents, while the promised utilities approach becomes extremely difficult and computationally intensive even with just one state variable or two agents.     

Capital market equilibrium with moral hazard and flexible technology

(Magill, M., Quinzii, M., 2002. Capital market equilibrium with moral hazard. Journal of Mathematical Economics 38, 149–190) showed that, in a stockmarket economy with private information, the moral hazard problem may be resolved provided that a spanning overlap condition is satisfed. This result depends on the assumption that the technology is given by a stochastic production function with a single scalar input. The object of the present paper is to extend the analysis of Magill and Quinzii to the case of multiple inputs. We show that their main result extends to this general case if and only if, for each firm, the number of linearly independent combinations of securities having payoffs correlated with, but not dependent on, the firms output is equal to the number of degrees of freedom in the firm’s production technology.     

Contracting under ex post moral hazard and non-commitment

This paper characterizes the optimal insurance contract in an environment where an informed agent can misrepresent the state of the world to a principal who cannot credibly commit to an auditing strategy. Because the principal cannot commit, the optimal strategy of the agent is not to tell the truth all the time. Assuming that there are T > 1 possible losses, and that the agent cannot fake an accident (he is constrained only to misreport the size of the loss when a loss occurs), the optimal contract is such that higher losses are over-compensated while lower losses are on average under-compensated. The amount by which higher losses are over-compensated decreases as the loss increases. The optimal contract may then be represented as a simple combination of a deductible, a lump-sum payment and a coinsurance provision.Received: 29 January 1999, Accepted: 26 June 2001, JEL Classification: D82, G2, C72.I would like to thank my dissertation committee Stanley Baiman, David Cummins, Georges Dionne, Neil Doherty and Sharon Tennyson (supervisor) for their insights, as well as Keith Crocker, Steve Coate, Richard Derrig, Michele Piccone and Pascale Viala. The financial help received during my doctoral studies from the Social Sciences and Humanities Research Council of Canada (SSHRC) and the S. S. Huebner Foundation are gratefully acknowledged. This research has been funded by the Fonds pour la Formation de Chercheurs et d'Aide à la Recherche (FCAR-Québec), SSHRC-Canada and the Risk Management Chair at HEC Montréal. The continuing financial support of CIRANO is also appreciated. I am responsible for all errors.     

Moral hazard,debt overhang and capital structure

This paper investigates the impact of managerial moral hazard on the debt overhang of a firm by constructing a contingent claims model in which the manager faces costly effort. Using a calibrated capital structure model, we show that the costs of debt overhang become more serious in the presence of managerial moral hazard. Such costs even account for more than half of the total agency costs at a high level of cash flow. Moreover, in contrast to the results of Hackbarth and Mauer (2012), our model predicts a U-shaped relationship between the leverage ratio and investment opportunities of a firm, which is caused by managers’ moral hazard. Finally, by considering this moral hazard, we also show the coexistence of low leverage ratios and high credit spreads, which explains the phenomenon of “low debt levels and high credit spreads” observed in practice.     

Securitization and optimal retention under moral hazard

Securitization improves liquidity in capital markets by allowing originators to remove issued loans from its balance sheet and use the proceeds for other purposes. Securitization is often suspected of being one of the main reasons for the recent financial crisis. One concern is that securitization leads to moral hazard in lender screening and monitoring. By selling loans to investors and removing them from their books, banks have a lesser incentive to carefully evaluate and monitor borrowers’ credit quality to ensure that they can repay their loans. One problem in the literature is that the analysis of securitization is very general and suffers from a lack of specific security design analysis under asymmetric information. We address the moral hazard problem using a principal–agent model where the investor is the principal and the lender is the agent. We show that the optimal contract must contain a retention clause in the presence of moral hazard. The optimal retention is affected by tranching and credit enhancement.     

A two-stage segment and prediction model for mortgage prepayment prediction and management

Predicting the risk of mortgage prepayments has been the focus of many studies over the past three decades. Most of these works have used single prediction models, such as logistic regressions and survival models, to seek the key influencing factors. From the point of view of customer relationship management (CRM), a two-stage model (i.e., the segment and prediction model) is proposed for analyzing the risk of mortgage prepayment in this research. In the first stage, random forests are used to segment mortgagors into different groups; then, a proportional hazard model is constructed to predict the prepayment time of the mortgagors in the second stage. The results indicate that the two-stage model predicts mortgage prepayment more accurately than the single-stage model (non-segmentation model).     

Multivariate survival functions characterized by constant product of mean remaining lives and hazard rates

Under the assumption that the products of multivariate mean remaining lives and hazard rates are the same constant, it is shown that the corresponding multivariate survival function belongs to one of three families: (1) multivariate Gumbel exponential distribution; (2) multivariate Lomax (Pareto type II) distribution; (3) multivariate rescaled Dirichlet distribution. This result is then used to derive another characterization of the latter two families based on the residual life distribution.     

浅析合成氨装置的火灾危险源及火灾控制措施

塔西南化肥厂合成氨装置以天然气为原料,采用M.W凯洛格公司提供的低能耗、加压催化转化法生产合成氨,生产过程中涉及的危险物料也比较多,如天然气、氢气、一氧化碳、氨等,一旦发生火灾,火势迅速扩大,扑救困难,损失严重。文章针对合成氨装置的火灾危险源进行分析,提出了装置火灾预防和控制措施以及生产过程中的防火安全注意事项。     

网上银行业务风险评价模型及其控制研究

文章分析了网上银行的风险,建立了包括风险识别、风险分析、风险模型和风险防范等多个要素组成的网上银行业务风险的评价和控制模型,针对风险评价,提出了动态获取随时间变化的参数,获得单点的危险率,计算总体的危险率的一种新方法。     

Multivariate distributions characterized by a relationship between mean residual life and hazard rate

In this paper, we characterize some multivariate distributions based on a relationship between the multivariate hazard rate, as defined by Johnson and Kotz (1975) and Marshall (1975), and the multivariate mean residual life as defined by Arnold and Zahedi (1988). The results are extensions of the results obtained earlier by Roy (1989, 1990) and Ma (1996, 1997). Received July 1997     

我国动物源性食品质量安全问题、危害及其监管对策

本文简要介绍了当前我国动物源性食品存在的主要质量安全问题,并对其进行了危害性分析,同时就新形势下全面加强动物源性食品质量安全管理提出了相应的对策。