This paper argues that we ought to rethink the harm-reduction prioritization strategy that has shaped early responses to acute resource scarcity (particularly of intensive care unit beds) during the COVID-19 pandemic. Although some authors have claimed that “[t]here are no egalitarians in a pandemic,” it is noted here that many observers and commentators have been deeply concerned about how prioritization policies that proceed on the basis of survival probability may unjustly distribute the burden of mortality and morbidity, even while reducing overall deaths. The paper further argues that there is a general case in favor of an egalitarian approach to medical rationing that has been missed in the ethical commentary so far; egalitarian approaches to resource rationing minimize wrongful harm. This claim is defended against some objections and the paper concludes by explaining why we should consider the possibility that avoiding wrongful harm is more important than avoiding harm simpliciter.

Innovations in medicine provide us longer and healthier life, leading lower mortality. Sooner rather than later, much greater longevity would be possible for us due to artificial intelligence advances in health care. Similarly, Advanced Driver Assistance Systems (ADAS) in highly automated vehicles may reduce or even eventually eliminate accidents by perceiving dangerous situations, which would minimize the number of accidents and lead to fewer loss claims for insurance companies. To model the survivor function capturing greater longevity as well as the number of claims reflecting less accidents in the long run, in this paper, we study a Cox process whose intensity process is piecewise-constant and decreasing. We derive its ultimate distributional properties, such as the Laplace transform of intensity integral process, the probability generating function of point process, their associated moments and cumulants, and the probability of no more claims for a given time point. In general, this simple model may be applicable in many other areas for modeling the evolution of gradually disappearing events, such as corporate defaults, dividend payments, trade arrivals, employment of a certain job type (e.g., typists) in the labor market, and release of particles. In particular, we discuss some potential applications to insurance.

We study the asymptotic behavior of the survival probability of a multi-type branching process in a random environment. In the one-dimensional situation, the class of processes considered corresponds to the strongly subcritical case. We also prove a conditional limit theorem describing the distribution of the number of particles in the process given its survival for a long time.

In this paper, we propose an estimator of the survival probability for a Lévy risk model observed at low frequency. The estimator is constructed via a regularised version of the inverse of the Laplace transform. The convergence rate of the estimator in a sense of the integrated squared error is studied for large sample size. Simulation studies are also given to show the finite sample performance of our estimator.

Remaining jaguar Panthera onca populations in the Atlantic Forest are restricted to eight regions, and all populations appear to be declining. We report on the status of one of the last populations in south-eastern Brazil. We monitored this population with camera traps during June 2005–January 2013 in Vale Natural Reserve. We estimated an abundance of 9 ± SE 1.98 jaguars (95% CI 9–17) and a population density of 3.22 ± SE 1.58 individuals per 100 km2 (95% CI 1.29–7.98). Annual survival probability over a 5-year interval was 78% (95% CI 58–98) and the recapture probability was 62% (95% CI 42–79). Although our results are among the highest densities reported for the jaguar in this biome, the future of the population is threatened by genetic deterioration and local threats, including the expansion of an existing highway and depletion of the jaguar's native prey base as a result of poaching, and will depend upon urgent implementation of conservation actions. The necessary actions include establishing gene flow with other compatible populations, increasing surveillance against poaching, continuing population monitoring of jaguars and their main prey species, and implementing mitigation measures in relation to the impacts of the highway on local fauna.

We study the asymptotics of the survival probability for the critical and decomposable branching processes in a random environment and prove Yaglom-type limit theorems for these processes. It is shown that such processes possess some properties having no analogues for the decomposable branching processes in a constant environment.

Given an autoregressive process X of order p(i.e.Xn = a1Xn−1 + ··· + apXn−p + Ynwhere the random variables Y1, Y2,... are i.i.d.), we study the asymptotic behaviour of the probability that the processdoes not exceed a constant barrier up to time N (survival or persistenceprobability). Depending on the coefficients a1,...,ap and the distribution ofY1, we state conditions under which the survival probabilitydecays polynomially, faster than polynomially or converges to a positive constant. Specialemphasis is put on AR(2) processes.

We derive a variety of estimates for the survival probability of a branching process in a random environment. There are three cases of interest, the critical, weakly and strongly subcritical. The large deviation result, first obtained by Dekking for the class of finite state space i.i.d. environments, is shown to hold in more general environments. We also obtain some finer convergence results.

In this paper we derive formulae for finite time survival probabilities when the aggregate claims process is a Gamma process. We illustrate how a compound Poisson process can be approximated by a Gamma process and by a process defined as a translated Gamma process. We also show how survival probabilities for a compound Poisson process can be approximated by those for a Gamma process or a translated Gamma process.

In this paper we present an algorithm for the approximate calculation of finite time survival probabilities for the classical risk model. We also show how this algorithm can be applied to the calculation of infinite time survival probabilities. Numerical examples are given and the stability of the algorithms is discussed.

We determine the decay rate of the survival probability of subcritical branching processes in a two-state random environment, where one state is subcritical, the other supercritical. This result is applied to obtain the asymptotic behavior (as n →∞) of the number of different words of length n occurring on the binary, and generally the b-ary, tree with Bernoulli percolation.

We consider an individual which performs a diffusive motion in a certain state space and dies according to a state-dependent death rate. An integral equation for the survival probability is derived, and finally a sufficient criterion for the existence of an initial state is given, for which the corresponding individual dies with probability one.