Exact joint laws associated with spectrally negative Levy processes and applications to insurance risk theory

We consider the spectrally negative Levy processes and determine the joint laws for the quantities such as the first and last passage times over a fixed level, the overshoots and undershoots at first passage, the minimum, the maximum and the duration of negative values. We apply our results to insurance risk theory to find an explicit expression for the generalized expected discounted penalty function in terms of scale functions. Further, a new expression for the generalized Dickson's formula is provided.Comment: To appear in Front. Math. Chin

Convexity of ruin probability and optimal dividend strategies for a general Levy process

In this paper, we consider the optimal dividends problem for a company whose cash reserves follow a general Levy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we appeal to very recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin. We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy.Comment: 19 pages, corrected some typo

On optimality of the barrier strategy for a general Levy risk process

We consider the optimal dividend problem for the insurance risk process in a general Levy process setting. The objective is to find a strategy which maximizes the expected total discounted dividends until the time of ruin. We give sufficient conditions under which the optimal strategy is of barrier type. In particular, we show that if the Levy density is a completely monotone function, then the optimal dividend strategy is a barrier strategy. This approach was inspired by the work of Avram et al. (2007) [Annals of Applied Probability 17, 156-180], Loeffen (2008) [Annals of Applied Probability 18, 1669-1680] and Kyprianou et al. (2010) [Journal of Theoretical Probability 23, 547-564] in which the same problem was considered under the spectrally negative Levy processes setting.Comment: 14 page

Immunoregulatory Protein Profiles of Necrotizing Enterocolitis versus Spontaneous Intestinal Perforation in Preterm Infants

Necrotizing enterocolitis (NEC) and spontaneous intestinal perforation (SIP) are the most common acute surgical emergencies associated with high morbidity and mortality in preterm infants. We aimed to compare the profiles of immunoregulatory proteins and identify novel mediators in plasma of NEC and SIP infants. We also investigated the expression of target genes in resected intestinal tissues and an enterocyte cell line. Using Cytokine Antibody Array assay, we reported the first comparative profiles of immunoregulatory proteins in plasma of NEC and SIP infants, and showed that dysregulated proteins belonged to functionally diversified categories, including pro- and anti-inflammation, angiogenesis, cell growth, wound healing, anti-apoptosis, cell adhesion and extracellular matrix reorganization. Validation by ELISA confirmed significantly higher concentrations of interleukin (IL)-6, angiopoietin (Ang)-2, soluble type II interleukin-1 receptor (sIL-1RII), and soluble urokinase-type plasminogen activator receptor (suPAR) in NEC infants compared with gestational age-matched control, and a lower level of an epidermal growth factor receptor, secreted form of receptor tyrosine-protein kinase ErbB3 (sErbB3), compared with SIP infants. mRNA expressions of IL1-RII and uPAR were up-regulated in resected bowel tissues from NEC infants, indicating that immunoregulation also occurred at the cellular level. In FHs-74 Int cells, Ang-2, IL1-RII and uPAR mRNA expressions were significantly induced by the combined treatment with lipopolysaccharide (LPS) and platelet activating factor (PAF). Our study provided plasmatic signatures of immunoregulatory proteins in NEC and SIP infants, and demonstrated involvement of multiple functional pathways. The magnitude of changes in these proteins was significantly more extensive in NEC infants, reflecting the different nature of injury and/or severity of inflammation. We speculate that dysregulation of IL-6, Ang-2, IL-1RII and uPAR occurred at both systemic and cellular levels, and probably mediated via LPS and endogeneous PAF signals. Such exaggerated immunologic responses may account for the high morbidity and mortality in NEC compared with SIP patients

Alternative approach to the optimality of the threshold strategy for spectrally negative Levy processes

Consider the optimal dividend problem for an insurance company whose uncontrolled surplus precess evolves as a spectrally negative Levy process. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. Kyprianou, Loeffen and Perez [28] have shown that a refraction strategy (also called threshold strategy) forms an optimal strategy under the condition that the Levy measure has a completely monotone density. In this paper, we propose an alternative approach to this optimal problem.Comment: 16 page

Goodness-of-fit tests for the cox proportional hazards model via bootstrap method

Bibliography: p. 141-145

Some aspects of mean residual life

Bibliography: p. 92-94