Some Aspects of Cumulative Risk

The classical treatment of stochastic models in non-life insurance is to first derive the well-known Poisson distribution by considering the question of how many claims take place during a definite period t. In deriving this distribution the following three assumptions are made: ( I) The population studied is homogeneous. ( II) The occurrence of a claim is a rare event, viz. in an infinite-simal time interval [t, t + Δt], the probability of more than one occurrence must be of the order of magnitude o(Δt). (III) The occurrence of any later claim is not influenced by previous ones (no contagion). In my purely theoretical study [5]), the consequences of discarding one or more of the above assumptions were considered. By so generalizing the Poisson distribution, a great many stochastic models can be built, although the results were not always successful. The following study concentrates on some considerations based on assumption (II). The theoretical formulation of the model will be dealt with briefly and the author would first make reference to the instructive article of Thyrion [7] which was unfortunately unknown to him when he was preparing his already mentioned paper. Ammeter [2] and Arfwedson [3] have also considered special cases of this generalization. With the help of the statistics over traffic accidents in the city of Zurich, I hope to throw some more light on the practical aspects of the problem. To the Statistics Office of this city I would express my thanks for kindly placing all documents at my disposa

Contributions to the Theory of the Largest Claim Cover

In the wake of the technical development of our era we are increasingly faced with claims of extremely large amounts. Whereas even in the past century large claims were mostly due to elemental or natural forces such as earthquakes, hurricanes and floods, there are today other causes, conditioned by human factors, that have considerably increased in importance. Another fact to be observed is that the risks that are passed on to the insurance market assume a more serious character year by year. Large building complexes, giant tankers, containers, atomic power stations, dams and jumbo jets pose for the insurers problems which are in no way easy to solve, since the risk covers required touch the limits of market capacity and their rating is subject to great uncertainties. At the same time, the readiness to underwrite such covers is a matter of utmost importance for the private insurance industry. For the coverage of such large risks, various insurance forms have been developed in the past years within the range of non-proportional methods. Besides the excess of loss and stop loss covers in their usual form, the cumulative loss cover and the largest claim cover have attracted particular attention. The cumulative risk cover has, for example, been dealt with in [11]) and has also been frequently offered in practice. The coverage of the largest claim or, more generally, of the sum of the n largest claims does not appear to have gained a proper foothold in practice in spite of various valuable contributions in this field—considering particularly [2], [3], [5], [8] and [14]. The fact that it was during 1963/64 that various authors analysed these problems is no coincidence, for it was then that in two ASTIN Colloquia these topics were discusse

The recent Development of Risk Theory and its Applications

The response to the invitation for the 5th Colloquium has been, especially for subject 1, very gratifying; a large number of meritorious papers have been sent in. Fortunately, it took not much time in this case to find a good guide for all this work. R. E. Beard presents in his article "Some Actuarial Aspects of Non-Life Insurance Company Management”) a broad cross-section of the many problems that confront the non-life insurer. It was therefore regarded as not quite unwise to follow his steps and to discuss the other papers at suitable points. In the first half of his work R. E. Beard deals with a practical example from motor insurance, which is fully calculated with the help of numerical data. The question relates to the estimation of the value of outstanding claims, a quantity which is of decisive importance for the evaluation of the results of a portfolio. Apart from chance fluctuations which might affect the statistics from year to year, there are three major factors that render the task of estimation difficult: (a) the natural growth of the portfolio (b) the fact that bigger claims require longer time for settlement than the smaller ones (c) the change in the value of money with tim

Duality for pathwise superhedging in continuous time

We provide a model-free pricing-hedging duality in continuous time. For a frictionless market consisting of $d$ risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging price of a path dependent European option has the same value as the purely probabilistic problem of finding the supremum of the expectations of the option over all martingale measures. The superhedging problem is formulated with simple trading strategies, the claim is the limit inferior of continuous functions, which allows for upper and lower semi-continuous claims, and superhedging is required in the pathwise sense on a $\sigma$-compact sample space of price trajectories. If the sample space is stable under stopping, the probabilistic problem reduces to finding the supremum over all martingale measures with compact support. As an application of the general results we deduce dualities for Vovk's outer measure and semi-static superhedging with finitely many securities

Explaining heterogeneity in the predictive value of Type D personality for cardiac events and mortality

AbstractBackgroundType D personality has been associated with adverse outcomes in patients with coronary artery disease (CAD). However, large heterogeneity exists between Type D studies, including some studies reporting null-findings.ObjectivesThe aim of this study was to examine i) choice of endpoint and ii) age as two study characteristics that may partly explain this large heterogeneity in the Type D associated prognostic effect.MethodsWe used four existing data cohorts of 1503 CAD patients (89% male, mean age=57.2±9.1) with baseline measures of Type D and endpoints >5years follow-up: major adverse cardiac events (MACE), cardiac death/MI, and non-cardiac death. Patients were classified in 4 age categories: <50y, 50–59y, 60–69y and ≥70y. Multiple logistic regression models included age, sex, and clinical covariates.ResultsAt follow-up, there were 295 events, including 116 cardiac death/MI, and 37 non-cardiac deaths. Both continuous and categorical measures of Type D predicted adverse events. Type D was independently associated with MACE (OR=1.82; 95%CI 1.33–2.50) and cardiac death/MI (OR=2.49; 95%CI 1.55–3.99). However, Type D was not associated with non-cardiac death (OR=1.23; 95%CI 0.57–2.69). Regarding age, Type D consistently predicted MACE in the lower age groups (all ORs≥2.20, all ps≤.004), but not in patients aged ≥70y (OR=1.43, p=.57).ConclusionsChoice of endpoint and age modulated the risk conferred by Type D personality. Type D was associated with an increased risk of cardiac events, but not with non-cardiac death, or with events in patients aged ≥70y. Research on psychosocial risk in CAD should account for different sources of heterogeneity in study characteristics

Characteristics of ADHD symptom response/remission in a clinical trial of methylphenidate extended release

Clinical trials in attention-deficit/hyperactivity disorder (ADHD) have typically measured outcome using clinician ratings on the Attention-Deficit/Hyperactivity Disorder Rating Scale, Fourth Edition (ADHD-RS-IV) and the Clinical Global Impression-Improvement (CGI-I) scale. Remission has been defined as an endpoint score of less than or equal to 18 on the ADHD-RS-IV (or a mean score of 1). Responders have been defined as patients who achieve a CGI-I score of much or very much improved (1 or 2). There is a lack of agreement in the literature on what percent change in symptoms on the ADHD-RS-IV should be used to define improvement or remission. This study uses data from a clinical trial of a methylphenidate extended release (MPH-MLR; Aptensio XR&#174;) phase III clinical trial to attempt to determine the percent change of symptoms that best corresponds with improvement and remission. Symptom remission at endpoint (ADHD-RS-IV total score &#8804;18) was most closely aligned with a &#8805;46% reduction in ADHD-RS-IV total score. Clinical improvement was most closely aligned with a &#8805;40% reduction in ADHD-RS-IV total score. The three different measures of outcome were strongly aligned during double blind and open label treatment, and were independent of subtype status. Our data suggest that at least 40% improvement in symptoms is needed to achieve a robust response at endpoint

A review and conceptual model of the association of Type D personality with suicide risk

The role of personality as distal risk factor for suicidal thoughts and behavior is still unclear. This review aims to propose two conceptual models that explain the psychological plausibility of Type D personality as distal risk factor and contributor to the transition from general to suicide distress. To support this aim, we performed a systematic review of existing studies on the association between Type D personality and suicidal distress. A systematic search yielded eight studies that reported on Type D personality and suicidal distress. Type D personality was robustly associated with suicidal thoughts and behaviors, across populations and countries. Type D was related to the level/frequency of suicidal ideation in seven studies, and suicide attempt in two studies. Our first theoretical model identifies intra-psychic (depression, alcohol misuse, posttraumatic stress) and interpersonal (low belonging, social isolation, lack of support) vulnerabilities of individuals with Type D that may fuel the development of suicidal thoughts and behaviors. Type D by itself will not account for why people become suicidal, but our second theoretical model suggests that the avoidant-passive tendencies of Type D individuals may result in persistent problem-solving deficits, and, eventually, feelings of entrapment that may contribute to the desire to escape from pain. We conclude that empirical evidence supports the hypothesized link between Type D personality, and suicidal thoughts and behaviors. Our conceptual models – albeit often supported by indirect evidence - further substantiate the plausibility of this link, and offer concrete guidance for future studies. Primarily, more longitudinal research is necessary