On optimality of the barrier strategy in de Finetti's dividend problem for spectrally negative L\'{e}vy processes

We consider the classical optimal dividend control problem which was proposed by de Finetti [Trans. XVth Internat. Congress Actuaries 2 (1957) 433--443]. Recently Avram, Palmowski and Pistorius [Ann. Appl. Probab. 17 (2007) 156--180] studied the case when the risk process is modeled by a general spectrally negative L\'{e}vy process. We draw upon their results and give sufficient conditions under which the optimal strategy is of barrier type, thereby helping to explain the fact that this particular strategy is not optimal in general. As a consequence, we are able to extend considerably the class of processes for which the barrier strategy proves to be optimal.Comment: Published in at http://dx.doi.org/10.1214/07-AAP504 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Refracted Lévy processes

Motivated by classical considerations from risk theory, we investigate boundary crossing problems for refracted Lévy processes. The latter is a Lévy process whose dynamics change by subtracting off a fixed linear drift (of suitable size) whenever the aggregate process is above a pre-specified level. More formally, whenever it exists, a refracted Lévy process is described by the unique strong solution to the stochastic differential equation dUt =−δ1{Ut>b} dt + dXt, where X ={Xt: t ≥ 0} is a Lévy process with law P and b,δ ∈ R such that the resulting process U may visit the half line (b, ∞) with positive probability. We consider in particular the case that X is spectrally negative and establish a suite of identities for the case of one and two sided exit problems. All identities can be written in terms of the q-scale function of the driving Lévy process and its perturbed version describing motion above the level b. We remark on a number of applications of the obtained identities to (controlled) insurance risk processes

The equivalence of two tax processes

We introduce two models of taxation, the latent and natural tax processes, which have both been used to represent loss-carry-forward taxation on the capital of an insurance company. In the natural tax process, the tax rate is a function of the current level of capital, whereas in the latent tax process, the tax rate is a function of the capital that would have resulted if no tax had been paid. Whereas up to now these two types of tax processes have been treated separately, we show that, in fact, they are essentially equivalent. This allows a unified treatment, translating results from one model to the other. Significantly, we solve the question of existence and uniqueness for the natural tax process, which is defined via an integral equation. Our results clarify the existing literature on processes with tax

FIRST PASSAGE TIMES OVER STOCHASTIC BOUNDARIES FOR SUBDIFFUSIVE PROCESSES

Let X = ( X t ) t ≥ 0 \mathbb {X}=(\mathbb {X}_t)_{t\geq 0} be the subdiffusive process defined, for any t ≥ 0 t\geq 0 , by X t = X ℓ t \mathbb {X}_t = X_{\ell _t} where X = ( X t ) t ≥ 0 X=(X_t)_{t\geq 0} is a Lévy process and ℓ t = inf { s &gt; 0 ; K s &gt; t } \ell _t=\inf \{s&gt;0; \mathcal {K}_s&gt;t \} with K = ( K t ) t ≥ 0 \mathcal {K}=(\mathcal {K}_t)_{t\geq 0} a subordinator independent of X X . We start by developing a composite Wiener-Hopf factorization to characterize the law of the pair ( T a ( b ) , ( X − b ) T a ( b ) ) (\mathbb {T}_a^{({b})}, (\mathbb {X} - {b})_{\mathbb {T}_a^{({b})}}) where T a ( b ) = inf { t &gt; 0 ; X t &gt; a + b t } \begin{equation*}\mathbb {T}_a^{({b})} = \inf \{t&gt;0; \mathbb {X}_t &gt; a+ {b}_t \} \end{equation*} with a ∈ R a \in \mathbb {R} and b = ( b t ) t ≥ 0 {b}=({b}_t)_{t\geq 0} a (possibly degenerate) subordinator independent of X X and K \mathcal {K} . We proceed by providing a detailed analysis of the cases where either X \mathbb {X} is a self-similar or is spectrally negative. For the later, we show the fact that the process ( T a ( b ) ) a ≥ 0 (\mathbb {T}_a^{({b})})_{a\geq 0} is a subordinator. Our proofs hinge on a variety of techniques including excursion theory, change of measure, asymptotic analysis and on establishing a link between subdiffusive processes and a subclass of semi-regenerative processes. In particular, we show that the variable T a ( b ) \mathbb {T}_a^{({b})} has the same law as the first passage time of a semi-regenerative process of Lévy type, a terminology that we introduce to mean that this process satisfies the Markov property of Lévy processes for stopping times whose graph is included in the associated regeneration set.</p

Replication, Pathogenesis and Transmission of Pandemic (H1N1) 2009 Virus in Non-Immune Pigs

The declaration of the human influenza A pandemic (H1N1) 2009 (H1N1/09) raised important questions, including origin and host range [1,2]. Two of the three pandemics in the last century resulted in the spread of virus to pigs (H1N1, 1918; H3N2, 1968) with subsequent independent establishment and evolution within swine worldwide [3]. A key public and veterinary health consideration in the context of the evolving pandemic is whether the H1N1/09 virus could become established in pig populations [4]. We performed an infection and transmission study in pigs with A/California/07/09. In combination, clinical, pathological, modified influenza A matrix gene real time RT-PCR and viral genomic analyses have shown that infection results in the induction of clinical signs, viral pathogenesis restricted to the respiratory tract, infection dynamics consistent with endemic strains of influenza A in pigs, virus transmissibility between pigs and virus-host adaptation events. Our results demonstrate that extant H1N1/09 is fully capable of becoming established in global pig populations. We also show the roles of viral receptor specificity in both transmission and tissue tropism. Remarkably, following direct inoculation of pigs with virus quasispecies differing by amino acid substitutions in the haemagglutinin receptor-binding site, only virus with aspartic acid at position 225 (225D) was detected in nasal secretions of contact infected pigs. In contrast, in lower respiratory tract samples from directly inoculated pigs, with clearly demonstrable pulmonary pathology, there was apparent selection of a virus variant with glycine (225G). These findings provide potential clues to the existence and biological significance of viral receptor-binding variants with 225D and 225G during the 1918 pandemic [5]

Comparison of Schmallenberg virus antibody levels detected in milk and serum from individual cows

BACKGROUND: Schmallenberg virus (SBV) is a recently emerged virus of ruminants in Europe. Enzyme-linked immunosorbent assays (ELISA) are commonly used to detect SBV-specific antibodies in bulk tank milk samples to monitor herd exposure to infection. However, it has previously been shown that a bulk tank milk sample can test positive even though the majority of cows within the herd are seronegative for SBV antibodies. Development of a pen-side test to detect antibodies in individual milk samples would potentially provide a cheaper test (for which samples are obtained non-invasively) than testing individual serum samples by ELISA. Therefore, the aim of this study was to investigate the agreement between antibody levels measured in milk and serum. RESULTS: Corresponding milk and serum samples from 88 cows in two dairy herds in the UK were tested for presence of immunoglobulin G antibodies to SBV using a commercially-available indirect ELISA. A serum neutralisation test (NT) was also performed as a gold standard assay. The ELISA values obtained for the bulk tank milk samples corresponded with the mean values for individual milk samples from each herd (bulk tank milk values were 58% and 73% and mean individual milk values 50% and 63% for herds A and B, respectively). Of the 88 serum samples tested in the NT, 82 (93%) were positive. Although at higher antibody levels, the ELISA values tended to be higher for the individual milk samples than for the corresponding serum samples, the positive predictive value for milk samples was 98% and for serum samples 94%. The serum ELISA was more likely to give false positive results around the lower cut-off value of the assay. CONCLUSIONS: The results indicate that testing of individual milk samples for antibodies against SBV by ELISA could be used to inform decisions in the management of dairy herds such as which, if any, animals to vaccinate

How to recognize inborn errors of immunity in a child presenting with a malignancy: guidelines for the pediatric hemato-oncologist

Inborn errors of immunity (IEI) are a group of disorders caused by genetically determined defects in the immune system, leading to infections, autoimmunity, autoinflammation and an increased risk of malignancy. In some cases, a malignancy might be the first sign of an underlying IEI. As therapeutic strategies might be different in these patients, recognition of the underlying IEI by the pediatric hemato-oncologist is important. This article, written by a group of experts in pediatric immunology, hemato-oncology, pathology and genetics, aims to provide guidelines for pediatric hemato-oncologists on how to recognize a possible underlying IEI and what diagnostic tests can be performed, and gives some consideration to treatment possibilities