Budget-constrained optimal insurance with belief heterogeneity

We re-examine the problem of budget-constrained demand for insurance indemnification when the insured and the insurer disagree about the likelihoods associated with the realizations of the insurable loss. For ease of comparison with the classical literature, we adopt the original setting of Arrow (1971), but allow for divergence in beliefs between the insurer and the insured; and in particular for singularity between these beliefs, that is, disagreement about zero-probability events. We do not impose the no sabotage condition on admissible indemnities. Instead, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, which rules out ex post moral hazard issues that could otherwise arise from possible misreporting of the loss by the insured. Under a mild consistency requirement between these beliefs that is weaker than the Monotone Likelihood Ratio (MLR) condition, we characterize the optimal indemnity and show that it has a simple two-part structure: full insurance on an event to which the insurer assigns zero probability, and a variable deductible on the complement of this event, which depends on the state of the world through a likelihood ratio. The latter is obtained from a Lebesgue decomposition of the insured’s belief with respect to the insurer’s belief.     

道德风险影响下的保险最优投资研究

在考虑道德风险的情况下,以均值方差准则为目标研究保险人最优投资问题.假设保险盈余过程服从C-L模型,金融市场上存在一种无风险资产和一种风险资产可供投资,其中风险资产的价格过程服从几何布朗运动.在纯道德风险保险契约设计中,借鉴相关研究对努力水平和效用化努力成本的假设,量化道德风险对盈余过程的影响.在均值方差目标下,建立保险人最优投资问题的广义Hamilton-Jacobi-Bellman(HJB)方程,给出保险人时间一致的均衡投资策略和价值函数.结果显示累计索赔比例参数越大,公司对最优努力水平越敏感,采取措施降低道德风险有利于公司收益提升;努力成本参数越大,公司会降低努力水平减少支出,避免损失.     

Analyzing continuous state space failure time processes: Two further results*

In a recent paper, Petersen (1988) considered a continuous state space failure time process. The central result provided in that paper was that the destination‐specific rate of transition of the process can be specified in two steps. First, one specifies the overall rate at which a change occurs. Then, one specifies the probability density function of the destination state, given that a transition occurred. This two‐step property was used in deriving the likelihood of the data and was exploited for purposes of estimation. The overall rate of transition can be estimated from the data on durations between changes in the dependent variable. The density for the new value of the dependent variable, given a change, can be estimated from the data on the values of the dependent variable after the change.

This paper extends these results in two ways. First, it is shown that one can derive the likelihood of the process directly from the destination‐specific rate of transition, without going through its decomposition into the overall rate times the density of the destination state, given a transition. Once the likelihood is derived, estimation is comparatively straightforward. Second, it is shown how one can derive, at each point in time, a more standard regression function for the continuous dependent variable, where its value is expressed in terms of its conditional mean plus an error term.     

Some properties and applications of cumulative Kullback–Leibler information

The cumulative Kullback–Leibler information has been proposed recently as a suitable extension of Kullback–Leibler information to the cumulative distribution function. In this paper, we obtain various results on such a measure, with reference to its relation with other information measures and notions of reliability theory. We also provide some lower and upper bounds. A dynamic version of the cumulative Kullback–Leibler information is then proposed for past lifetimes. Furthermore, we investigate its monotonicity property, which is related to some new concepts of relative aging. Moreover, we propose an application to the failure of nanocomponents. Finally, in order to provide an application in image analysis, we introduce the empirical cumulative Kullback–Leibler information and prove an asymptotic result. Copyright © 2015 John Wiley & Sons, Ltd.     

Assessing the reliability of a nanocomponent using nanocrack growth

In nanoscience and nanotechnology, much attention has been given to the dual problem of designing nanocomponents with novel physical properties and how such nanocomponents can be fabricated. Receiving less attention has been the question of the nanocomponent's reliability; how does a nanocomponent fail and how long does a nanocomponent survive under typical operating conditions? High reliability is necessary to guarantee the advancement and utilization of nanocomponents due to the fact that they account for a high proportion of costs of newly designed nanosystems as well as multiscale systems. A nanocomponent is a component that is made of atoms, and its reliability is determined by these atoms. There are situations where it is hard or impossible to extract information from a nanocomponent about its relationship to its atoms. In this article, we assess the nanocomponent's reliability by using its physical properties. Specifically, it is known that nanocrack growth involves considerable statistical variability and such variability should be accounted for assessing growth. In this paper, we first provide a stochastic nanocrack growth model and then evaluate the reliability of a nanocomponent based on this model. Various properties of this model are obtained. We also evaluate the reliability of a nanocomponent under different assumptions on our proposed growth model. This paper is a modification of the extensive literature on modeling fatigue cracks in materials on a larger scale, applied to nanoscale where growth is not a function of cumulative stress on the component but related to the time to first exceedance of a threshold. Copyright © 2013 John Wiley & Sons, Ltd.     

On allocating redundancies to k‐out‐of‐ n reliability systems

For two components in series and one redundancy with their lifetimes following the proportional hazard models, we build the likelihood ratio order and the hazard rate order for lifetimes of the redundant systems. Also, for k ‐out‐of‐ n system with components’ lifetimes having the arrangement increasing joint density and the redundancies having identically distributed lifetimes, allocating more redundancies to weaker components is shown to help improve the system's reliability. Copyright © 2014 John Wiley & Sons, Ltd.     

How Does Diet Influence Our Lives? Evaluating the Relationship between Isotopic Signatures and Mortality Patterns in Italian Roman Imperial and Medieval Periods

The present research investigates the relationship between dietary habits and mortality patterns in the Roman Imperial and Medieval periods. The reconstructions of population dynamics and subsistence strategies provide a fascinating source of information for understanding our history. This is particularly true given that the changes in social, economic, political, and religious aspects related to the transition from the Roman period to the Middle Ages have been widely discussed. We analyzed the isotopic and mortality patterns of 616 individuals from 18 archeological sites (the Medieval Latium sites of Colonna, Santa Severa, Allumiere, Cencelle, and 14 Medieval and Imperial funerary contexts from Rome) to compile a survivorship analysis. A semi-parametric approach was applied, suggesting variations in mortality patterns between sexes in the Roman period. Nitrogen isotopic signatures influenced mortality in both periods, showing a quadratic and a linear effect for Roman Imperial and Medieval populations, respectively. No influence of carbon isotopic signatures has been detected for Roman Imperial populations. Conversely, increased mortality risk for rising carbon isotopic values was observed in Medieval samples.     

Evaluating the Thermal Hazard of Double-Base Propellant SQ-2 by Using Microcalorimetry Method

The thermal decomposition behavior of double‐base rocket propellant SQ‐2 was studied by a Calvet microcalorimeter at four different heating rates. The kinetic and thermodynamic parameters were obtained from the analysis of the heat flow curves. The critical temperature of thermal explosion (T_b), the self acceleration decomposition temperature (T_SADT), the adiabatic decomposition temperature rise (ΔT_ad), the time‐to‐explosion of adiabatic system (t), critical temperature of hot‐spot initiation (T_cr), critical thermal explosion ambient temperature (T_acr), safety degree (SD) and thermal explosive probability (P_TE) were presented to evaluate the thermal hazard of SQ‐2.     

The Use of Adiabatic Calorimetry for the Process Analysis and Safety Evaluation in Free Radical Polymerization

Adiabatic calorimetry is a technique that has been introduced as an important approach to hazard evaluation of exothermically reactive systems. In this paper the free radical polymerization of methyl methacrylate (MMA) has been studied. One of the most important aspects of MMA polymerization is its exothermicity and autoaccelerating behaviour, these characteristics can generate the occurrence of a runaway reaction.In a runaway situation the reacting system is close to adiabatic behaviour because it is unable to eliminate the heat that is being generated. An even worse situation can be reproduced in the laboratory with the Phi-Tec pseudo-adiabatic calorimeter. Process design parameters that are usually calculated from thermodynamic data or using semiempirical rules, such as adiabatic temperature rise or maximum attainable pressure, can be directly determined.The existence of the ceiling temperature has been experimentally demonstrated.This revised version was published online in November 2005 with corrections to the Cover Date.