Interest rate is one of the main risks for the liability of the variable annuity (VA) due to its long maturity. However, most existing studies on the risk measures of the VA assume a constant interest rate. In this paper, we propose an efficient two-dimensional willow tree method to compute the liability distribution of the VA with the joint dynamics of the mutual fund and interest rate. The risk measures can then be computed by the backward induction on the tree structure. We also analyze the sensitivity and impact on the risk measures with regard to the market model parameters, contract attributes, and monetary policy changes. It illustrates that the liability of the VA is determined by the long-term interest rate whose increment leads to a decrease in the liability. The positive correlation between the interest rate and mutual fund generates a fat-tailed liability distribution. Moreover, the monetary policy change has a bigger impact on the long-term VAs than the short-term contracts.

This study aims to identify the risk factors associated with mortality and survival of COVID-19 cases in a state of the Brazilian Northeast. It is a historical cohort with a secondary database of 2070 people that presented flu-like symptoms, sought health assistance in the state and tested positive to COVID-19 until 14 April 2020, only moderate and severe cases were hospitalised. The main outcome was death as a binary variable (yes/no). It also investigated the main factors related to mortality and survival of the disease. Time since the beginning of symptoms until death/end of the survey (14 April 2020) was the time variable of this study. Mortality was analysed by robust Poisson regression, and survival by Kaplan–Meier and Cox regression. From the 2070 people that tested positive to COVID-19, 131 (6.3%) died and 1939 (93.7%) survived, the overall survival probability was 87.7% from the 24th day of infection. Mortality was enhanced by the variables: elderly (HR 3.6; 95% CI 2.3–5.8; P < 0.001), neurological diseases (HR 3.9; 95% CI 1.9–7.8; P < 0.001), pneumopathies (HR 2.6; 95% CI 1.4–4.7; P < 0.001) and cardiovascular diseases (HR 8.9; 95% CI 5.4–14.5; P < 0.001). In conclusion, mortality by COVID-19 in Ceará is similar to countries with a large number of cases of the disease, although deaths occur later. Elderly people and comorbidities presented a greater risk of death.

Let $\{D_M\}_{M\geq 0}$ be the n-vertex random directed graph process, where $D_0$ is the empty directed graph on n vertices, and subsequent directed graphs in the sequence are obtained by the addition of a new directed edge uniformly at random. For each $$\varepsilon> 0$$, we show that, almost surely, any directed graph $D_M$ with minimum in- and out-degree at least 1 is not only Hamiltonian (as shown by Frieze), but remains Hamiltonian when edges are removed, as long as at most $1/2-\varepsilon$ of both the in- and out-edges incident to each vertex are removed. We say such a directed graph is $(1/2-\varepsilon)$-resiliently Hamiltonian. Furthermore, for each $\varepsilon > 0$, we show that, almost surely, each directed graph $D_M$ in the sequence is not $(1/2+\varepsilon)$-resiliently Hamiltonian.

This improves a result of Ferber, Nenadov, Noever, Peter and Škorić who showed, for each $\varepsilon > 0$, that the binomial random directed graph $D(n,p)$ is almost surely $(1/2-\varepsilon)$-resiliently Hamiltonian if $p=\omega(\log^8n/n)$.

For fixed graphs F1,…,Fr, we prove an upper bound on the threshold function for the property that G(n, p) → (F1,…,Fr). This establishes the 1-statement of a conjecture of Kohayakawa and Kreuter.

A software release game was formulated by Zeephongsekul and Chiera [Zeephongsekul, P. & Chiera, C. (1995). Optimal software release policy based on a two-person game of timing. Journal of Applied Probability 32: 470–481] and was reconsidered by Dohi et al. [Dohi, T., Teraoka, Y., & Osaki, S. (2000). Software release games. Journal of Optimization Theory and Applications 105(2): 325–346] in a framework of two-person nonzero-sum games. In this paper, we further point out the faults in the above literature and revisit the Nash equilibrium strategies in the software release games from the viewpoints of both silent and noisy type of games. It is shown that the Nash equilibrium strategies in the silent and noisy of software release games exist under some parametric conditions.

A classical result of Erdős and, independently, of Bondy and Simonovits [3] says that the maximum number of edges in an n-vertex graph not containing C2k, the cycle of length 2k, is O(n1+1/k). Simonovits established a corresponding supersaturation result for C2k’s, showing that there exist positive constants C,c depending only on k such that every n-vertex graph G with e(G)⩾ Cn1+1/k contains at least c(e(G)/v(G))2k copies of C2k, this number of copies tightly achieved by the random graph (up to a multiplicative constant).

In this paper we extend Simonovits' result to a supersaturation result of r-uniform linear cycles of even length in r-uniform linear hypergraphs. Our proof is self-contained and includes the r = 2 case. As an auxiliary tool, we develop a reduction lemma from general host graphs to almost-regular host graphs that can be used for other supersaturation problems, and may therefore be of independent interest.

In this paper we propose a polynomial-time deterministic algorithm for approximately counting the k-colourings of the random graph G(n, d/n), for constant d>0. In particular, our algorithm computes in polynomial time a $(1\pm n^{-\Omega(1)})$-approximation of the so-called ‘free energy’ of the k-colourings of G(n, d/n), for $k\geq (1+\varepsilon) d$ with probability $1-o(1)$ over the graph instances.

Our algorithm uses spatial correlation decay to compute numerically estimates of marginals of the Gibbs distribution. Spatial correlation decay has been used in different counting schemes for deterministic counting. So far algorithms have exploited a certain kind of set-to-point correlation decay, e.g. the so-called Gibbs uniqueness. Here we deviate from this setting and exploit a point-to-point correlation decay. The spatial mixing requirement is that for a pair of vertices the correlation between their corresponding configurations becomes weaker with their distance.

Furthermore, our approach generalizes in that it allows us to compute the Gibbs marginals for small sets of nearby vertices. Also, we establish a connection between the fluctuations of the number of colourings of G(n, d/n) and the fluctuations of the number of short cycles and edges in the graph.

Spontaneous abortion is considered a public health problem having several causes, including infections. Among the infectious agents, bacteria of the vaginal microbiota and Ureaplasma parvum have been associated with abortion, but their participation needs to be further elucidated. This study aims to evaluate the influence of Mollicutes on the development of spontaneous abortion. Women who underwent spontaneous abortion and those with normal birth (control) were studied. Samples of cervical mucus (CM) and placental tissue were collected to identify Mollicutes using the quantitative polymerase chain reaction methodology. Eighty-nine women who had a miscarriage and 20 women with normal pregnancies were studied. The presence of Mollicutes in placental tissue increased the chance of developing miscarriage sevenfold. The prevalence of U. parvum in women who experienced spontaneous abortion was 66.3% in placental tissue. A positive association was observed between the detection of U. parvum in samples of placental tissue and abortion. There was a significant increase in microbial load in placental tissue for M. hominis, U. urealyticum and U. parvum compared to the control group. Detection of U. parvum in CM in pregnant women can ascend to the region of the placental tissue and trigger a spontaneous abortion.

The majority of available US-published reports present populations with community spread in urban areas. The objective of this report is to describe a rural healthcare system's utilisation of therapeutic options available to treat Coronavirus Disease 2019 (COVID-19) and subsequent patient outcomes. A total of 150 patients were treated for COVID-19 at three hospitals in the Dakotas from 21 March 2020 to 30 April 2020. The most common pharmacological treatment regimens administered were zinc, hydroxychloroquine plus azithromycin and convalescent plasma. Adjunctive treatments included therapeutic anticoagulation, tocilizumab and corticosteroids. As of 1 June 2020, 127 patients have survived to hospital discharge, 12 patients remain hospitalised and 11 patients have expired. The efficacy of hydroxychloroquine and azithromycin use has yet to be determined but was not without risks of corrected QT interval prolongation and arrhythmias in our cohort. We did not appreciate any adverse effects that appeared related to tocilizumab or convalescent plasma administration in those patient subsets. These findings may provide insight into disease severity and treatment options in the rural setting with limited resources to participate in clinical trials and encourage larger comparative studies evaluating treatment efficacy.

The purpose of this paper is to identify a workhorse mortality model for the adult age range (i.e., excluding the accident hump and younger ages). It applies the “general procedure” (GP) of Hunt & Blake [(2014), North American Actuarial Journal, 18, 116–138] to identify an age-period model that fits the data well before adding in a cohort effect that captures the residual year-of-birth effects arising in the original age-period model. The resulting model is intended to be suitable for a variety of populations, but economises on the number of period effects in comparison with a full implementation of the GP. We estimate the model using two different iterative maximum likelihood (ML) approaches – one Partial ML and the other Full ML – that avoid the need to specify identifiability constraints.