Konstadinos Politis

Some New Bounds For The Renewal Function

In the literature, most of the bounds for the renewal function U(x) corresponding to a lifetime distribution F are given in terms of the first two moments of F only. The best general upper bound of this type is the one given in Lorden (1970). In the present article, we show that improved bounds can be obtained if one exploits the specific form of the distribution F. We derive a bound that improves upon Lordens, at least on an interval [0,a) with a ≤ ∞, and we give both sufficient and necessary conditions for this improvement to hold uniformly for x ≥ 0. Refined upper as well as lower bounds are given for the case where F belongs to a class of distributions with monotone aging or when the renewal density is monotone.

Approximations for the gerber-shiu expected discounted penalty function in the compound poisson risk model

In the classical risk model with initial capital u, let τ(u) be the time of ruin, X +(u) be the risk reserve just before ruin, and Y +(u) be the deficit at ruin. Gerber and Shiu (1998) defined the function m δ(u) =E[e−δ τ(u) w(X +(u), Y +(u)) 1 (τ(u) < ∞)], where δ ≥ 0 can be interpreted as a force of interest and w(r,s) as a penalty function, meaning that m δ(u) is the expected discounted penalty payable at ruin. This function is known to satisfy a defective renewal equation, but easy explicit formulae for m δ(u) are only available for certain special cases for the claim size distribution. Approximations thus arise by approximating the desired m δ(u) by that associated with one of these special cases. In this paper a functional approach is taken, giving rise to first-order correction terms for the above approximations.

Non-exponential bounds for stop-loss premiums and ruin probabilities

We present an inventory of non-exponential bounds for ruin probabilities and stop-loss premiums in the general Sparre-Andersen model (renewal model) of risk theory. Various additional bounds are given if one assumes that the ladder height distribution F associated with the risk process belongs to a certain class of distributions, in particular if it is concave or it exhibits a (positive or negative) aging property. In most cases, these bounds are shown to improve existing ones in the literature and/or possess the correct asymptotic behaviour when the distribution F is subexponential. Since in the classical (compound Poisson) risk model the ladder height distribution is always concave, all the bounds given in the paper are also valid for this model. Finally, in many cases the results of the paper are also valid for any compound geometric distribution.

Monotonicity properties and the deficit at ruin in the Sparre Andersen model

Let H u (y) be the (proper) distribution function of the deficit at ruin, given that ruin occurs with initial surplus u, in the Sparre Andersen model of risk theory. Dickson & dos Reis (1996) discussed the monotonicity of H u (y) as a function of u. In this paper, we obtain various monotonicity results for H u (y) and other related quantities for the decreasing/increasing failure rate (DFR/IFR) and the increasing/decreasing mean residual lifetime (IMRL/DMRL) classes of distributions. These results in particular extend and make more concrete the results of Dickson & dos Reis (1996) and Willmot & Lin (1998). A new class of distributions (increasing convolution ratio; ICR) is introduced. This class extends the well-known class of distributions with IFR. Specifically, we show that if the ladder height distribution F in the model is ICR, the ratio is a non-decreasing function of u, where ψ(u) denotes the ruin probability and . Further, we obtain generalizations (expressed in terms of the distribution of the deficit) of the well-known new worse than used (NWU) property of the probability of non-ruin.

A functional approach for ruin probabilities

In the classical risk model with Poisson arrivals, we study a functional approach which can be used to obtain new approximation formulae for the probability of ultimate ruin. In particular, we consider a map Φ between appropriate function spaces with Φ(f) = ψ, where f denotes the density of claim sizes in the model and ψ is the function that gives the associated infinite-time ruin probability, ψ(x), for a given initial surplus x. Suppose then that , represent two claim size densities in the model, with corresponding outputs ψ(0) and ψ(1) respectively, and that only ψ(0) is known analytically. By establishing that the map Φ has derivatives of any order, we can approximate ψ(1) by using ψ(0) and the derivatives of Φ, provided that are not “too far” from each other. Since the explicit formulae for high order derivatives of Φ are typically complicated, we explain how computer algebra can be used for the implementation of the method. We also discuss how the functional approach can be used to obtain approximations for other quantities of interest in risk theory and we carry out some numerical illustrations to investigate the accuracy of the approximations.

Intrathecal baclofen improves psychiatric symptoms in spasticity patients.

Abstract Symptoms of psychological distress are relatively common in spasticity patients as a result either of the primary central nervous system insult or as a reaction to the ensuing impairment. Intrathecal baclofen (ITB) is an established treatment for the spasticity with an unknown effect on the psychiatric symptoms. In this study, we evaluate the role of ITB in the amelioration of psychological distress symptoms in 15 patients who were not mentally disabled or psychotic. The patients were assessed with the Symptom Check List 90–Revised before and a mean of 12 months after ITB treatment. A significant improvement was noted at the subscales of positive symptoms total and anxiety. The anxiety subscale improvement was correlated with the ITB dose, but not with the reduction in the spasticity. An interesting trend was also noted in the subscales of general severity index, depression, and obsession-compulsion. The results show an additional beneficial effect of ITB and highlight the need of further clarification of the causative mechanism.

A Generalization of the Lundberg Condition in the Sparre Andersen Model and Some Applications

We generalize the well-known Lundberg condition for the existence of the adjustment coefficient, R, in the Sparre Andersen model of risk theory. The new condition is given in terms of the distribution of the deficit at ruin in that model. As an application of this condition, we show that the function e Ru ψ(u) is nonincreasing when the claim size distribution in the model has a decreasing failure rate. Further, we obtain some new bounds for ruin probabilities and stop-loss premiums that are easy to compute and we give some examples to compare these bounds against existing ones in the literature.

Variables affecting factors associated with primary headache

Primary headache syndromes’ development is associated with biological, psychological and social parameters. Factors such as daily habits, behavioral characteristics and sleep disorders also play an important role. We aim to identify the variables which affect the above factors. The study included 111 patients affected by primary headache. The patients were stratified into subgroups according to gender, age, occupation and headache type. Women attained higher scores than men in three of the evaluation rating scales and lower scores in the severity of dependence scale. Occupation was associated with SF36 and Hamilton anxiety scale. Unemployed had higher scores in Hamilton anxiety. Migraineurs and occupied individuals have lower SF36 scores. Women are associated with depression, anxiety and higher disability derived from headache. Men are more prone to dependence on opioids. Unemployment was linked with anxiety and well-being. The migraneurs presented a decreased level of quality of life.