On the problematic of reserving and stochastic loss models

Abstract Traditionally, the common reserving methods used by the non-life actuaries are based on the assumption that future claims are going to behave in the same way as they did in the past. There are two main sources of variability in the processus of development of the claims: the variability of the speed with which the claims are settled and the variability between the severity of the claims from different accident years. High changes in these processes will generate distortions in the estimation of the claims reserves. The main objective of this thesis is to provide an indicator which firstly identifies and quantifies these two influences and secondly to determine which model is adequate for a specific situation. Two stochastic models were analysed and the predictive distributions of the future claims were obtained. The main advantage of the stochastic models is that they provide measures of variability of the reserves estimates. The first model (PDM) combines one conjugate family Dirichlet - Multinomial with the Poisson distribution. The second model (NBDM) improves the first one by combining two conjugate families Poisson -Gamma (for distribution of the ultimate amounts) and Dirichlet Multinomial (for distribution of the incremental claims payments). It was found that the second model allows to find the speed variability in the reporting process and development of the claims severity as function of two above mentioned distributions' parameters. These are the shape parameter of the Gamma distribution and the Dirichlet parameter. Depending on the relation between them we can decide on the adequacy of the claims reserve estimation method. The parameters have been estimated by the Methods of Moments and Maximum Likelihood. The results were tested using chosen simulation data and then using real data originating from the three lines of business: Property/Casualty, General Liability, and Accident Insurance. These data include different developments and specificities. The outcome of the thesis shows that when the Dirichlet parameter is greater than the shape parameter of the Gamma, resulting in a model with positive correlation between the past and future claims payments, suggests the Chain-Ladder method as appropriate for the claims reserve estimation. In terms of claims reserves, if the cumulated payments are high the positive correlation will imply high expectations for the future payments resulting in high claims reserves estimates. The negative correlation appears when the Dirichlet parameter is lower than the shape parameter of the Gamma, meaning low expected future payments for the same high observed cumulated payments. This corresponds to the situation when claims are reported rapidly and fewer claims remain expected subsequently. The extreme case appears in the situation when all claims are reported at the same time leading to expectations for the future payments of zero or equal to the aggregated amount of the ultimate paid claims. For this latter case, the Chain-Ladder is not recommended.

Essays on the treatment of cash flows under stochastic interest rates

Abstract This paper shows how to calculate recursively the moments of the accumulated and discounted value of cash flows when the instantaneous rates of return follow a conditional ARMA process with normally distributed innovations. We investigate various moment based approaches to approximate the distribution of the accumulated value of cash flows and we assess their performance through stochastic Monte-Carlo simulations. We discuss the potential use in insurance and especially in the context of Asset-Liability Management of pension funds.

Cost limitation through constrained oviposition site in a plant-pollinator/seed predator mutualism

Mutualism often involves reciprocal exploitation due to individual selection for increased benefits even at the expense of the partner. Therefore, stability and outcomes of such interactions crucially depend on cost limitation mechanisms. In the plant, pollinator /seed predator interaction between Silene latifolia (Caryophyllaceae) and Hadena bicruris (Lepidoptera: Noctuidae), moths generate pollination benefits as adults but impose seed predation costs as larvae. We examined whether floral morphology limits over-exploitation by constraining oviposition site. Oviposition site varies naturally inside vs. outside the corolla tube, but neither its determinants nor its effect on the interaction have been investigated. In a common garden with plants originating from eight populations, corolla tube length predicted oviposition site, but not egg presence or pollination efficiency, suggesting that long corolla tubes constrain the moth to lay eggs on petals. Egg position was also predicted by the combined effect of corolla tube and moth ovipositor lengths, with shorter ovipositor than corolla tube resulting in higher probability for eggs outside. Egg position on a given plant was repeatable over different exposure nights. When egg position was experimentally manipulated, eggs placed on the petal resulted in significantly fewer successful fruit attacks compared with eggs placed inside the corolla tube, suggesting differences in egg/larval mortality. Egg position also differently affected larval mass, fruit mass and fruit development. Our results indicate that constraining oviposition site through a long corolla tube reduces seed predation costs suffered by the plant without negatively affecting pollination efficiency and, hence may act to limit over-exploitation. However, the net effects of corolla tube depth variation on this interaction may fluctuate with extrinsic factors affecting egg mortality, and with patterns of gene flow affecting trait matching between the interacting species. The intermediate fitness costs incurred by both plant and insect associated with the different egg positions may reduce selective pressures for this interaction to evolve towards antagonism, favouring instead a mutualistic outcome. While a role for oviposition site variation in cost limitation is a novel finding in this system, it may apply more generally also to other mutualisms involving pollinating seed predators.

Cost-effectiveness of temozolomide for the treatment of newly diagnosed glioblastoma multiforme.

AIM: To perform a systematic review on the costs and cost-effectiveness of concomitant and adjuvant temozolomide with radiotherapy for the treatment of newly diagnosed glioblastoma compared with initial radiotherapy alone. METHODS: Electronic databases were searched for relevant publications on costs and cost-effectiveness until October 2008. RESULTS: We found four relevant clinical trials, one cost study and two economic models. The mean survival benefit in the radiotherapy plus temozolomide group varied between 0.21 and 0.25 life-years. Treatment costs were between 27,365 euros and 39,092 euros. The costs of temozolomide amounted to approximately 40% of the total treatment costs. The incremental cost-effectiveness ratios found in the literature were 37,361 euros per life-year gained and 42,912 euros per quality-adjusted life-year gained. However, the models are not comparable because different outcomes are used (i.e., life-years and quality-adjusted life-years). CONCLUSION: Although the models are not comparable according to outcome, the incremental cost-effectiveness ratios found are within acceptable ranges. We concluded that despite the high temozolomide acquisition costs, the costs per life-year gained and the costs per quality-adjusted life-year gained are comparable with other accepted first-line treatments with chemotherapy in patients with cancer.

Dispersal routes reconstruction and the minimum cost arborescence problem.

We show that the dispersal routes reconstruction problem can be stated as an instance of a graph theoretical problem known as the minimum cost arborescence problem, for which there exist efficient algorithms. Furthermore, we derive some theoretical results, in a simplified setting, on the possible optimal values that can be obtained for this problem. With this, we place the dispersal routes reconstruction problem on solid theoretical grounds, establishing it as a tractable problem that also lends itself to formal mathematical and computational analysis. Finally, we present an insightful example of how this framework can be applied to real data. We propose that our computational method can be used to define the most parsimonious dispersal (or invasion) scenarios, which can then be tested using complementary methods such as genetic analysis.

Cost-effectiveness analysis of a European primary-care physician training in smoking cessation counseling.

BACKGROUND: Physician training in smoking cessation counseling has been shown to be effective as a means to increase quit success. We assessed the cost-effectiveness ratio of a smoking cessation counseling training programme. Its effectiveness was previously demonstrated in a cluster randomized, control trial performed in two Swiss university outpatients clinics, in which residents were randomized to receive training in smoking interventions or a control educational intervention. DESIGN AND METHODS: We used a Markov simulation model for effectiveness analysis. This model incorporates the intervention efficacy, the natural quit rate, and the lifetime probability of relapse after 1-year abstinence. We used previously published results in addition to hospital service and outpatient clinic cost data. The time horizon was 1 year, and we opted for a third-party payer perspective. RESULTS: The incremental cost of the intervention amounted to US$2.58 per consultation by a smoker, translating into a cost per life-year saved of US$25.4 for men and 35.2 for women. One-way sensitivity analyses yielded a range of US$4.0-107.1 in men and US$9.7-148.6 in women. Variations in the quit rate of the control intervention, the length of training effectiveness, and the discount rate yielded moderately large effects on the outcome. Variations in the natural cessation rate, the lifetime probability of relapse, the cost of physician training, the counseling time, the cost per hour of physician time, and the cost of the booklets had little effect on the cost-effectiveness ratio. CONCLUSIONS: Training residents in smoking cessation counseling is a very cost-effective intervention and may be more efficient than currently accepted tobacco control interventions.

Validation of a Low-Cost Human Papillomavirus Genotyping Assay Based on PGMY PCR and Reverse Blotting Hybridization with Reusable Membranes.

The genotyping of human papillomaviruses (HPV) is essential for the surveillance of HPV vaccines. We describe and validate a low-cost PGMY-based PCR assay (PGMY-CHUV) for the genotyping of 31 HPV by reverse blotting hybridization (RBH). Genotype-specific detection limits were 50 to 500 genome equivalents per reaction. RBH was 100% specific and 98.61% sensitive using DNA sequencing as the gold standard (n = 1,024 samples). PGMY-CHUV was compared to the validated and commercially available linear array (Roche) on 200 samples. Both assays identified the same positive (n = 182) and negative samples (n = 18). Seventy-six percent of the positives were fully concordant after restricting the comparison to the 28 genotypes shared by both assays. At the genotypic level, agreement was 83% (285/344 genotype-sample combinations; κ of 0.987 for single infections and 0.853 for multiple infections). Fifty-seven of the 59 discordant cases were associated with multiple infections and with the weakest genotypes within each sample (P < 0.0001). PGMY-CHUV was significantly more sensitive for HPV56 (P = 0.0026) and could unambiguously identify HPV52 in mixed infections. PGMY-CHUV was reproducible on repeat testing (n = 275 samples; 392 genotype-sample combinations; κ of 0.933) involving different reagents lots and different technicians. Discordant results (n = 47) were significantly associated with the weakest genotypes in samples with multiple infections (P < 0.0001). Successful participation in proficiency testing also supported the robustness of this assay. The PGMY-CHUV reagent costs were estimated at $2.40 per sample using the least expensive yet proficient genotyping algorithm that also included quality control. This assay may be used in low-resource laboratories that have sufficient manpower and PCR expertise.

Learning wind fields with multiple kernels

This paper presents multiple kernel learning (MKL) regression as an exploratory spatial data analysis and modelling tool. The MKL approach is introduced as an extension of support vector regression, where MKL uses dedicated kernels to divide a given task into sub-problems and to treat them separately in an effective way. It provides better interpretability to non-linear robust kernel regression at the cost of a more complex numerical optimization. In particular, we investigate the use of MKL as a tool that allows us to avoid using ad-hoc topographic indices as covariables in statistical models in complex terrains. Instead, MKL learns these relationships from the data in a non-parametric fashion. A study on data simulated from real terrain features confirms the ability of MKL to enhance the interpretability of data-driven models and to aid feature selection without degrading predictive performances. Here we examine the stability of the MKL algorithm with respect to the number of training data samples and to the presence of noise. The results of a real case study are also presented, where MKL is able to exploit a large set of terrain features computed at multiple spatial scales, when predicting mean wind speed in an Alpine region.

How Much Does It Cost? Optimization of Costs in Sequence Analysis of Social Science Data

One major methodological problem in analysis of sequence data is the determination of costs from which distances between sequences are derived. Although this problem is currently not optimally dealt with in the social sciences, it has some similarity with problems that have been solved in bioinformatics for three decades. In this article, the authors propose an optimization of substitution and deletion/insertion costs based on computational methods. The authors provide an empirical way of determining costs for cases, frequent in the social sciences, in which theory does not clearly promote one cost scheme over another. Using three distinct data sets, the authors tested the distances and cluster solutions produced by the new cost scheme in comparison with solutions based on cost schemes associated with other research strategies. The proposed method performs well compared with other cost-setting strategies, while it alleviates the justification problem of cost schemes.

Cost-effectiveness analysis of immune-modulating nutritional support for gastrointestinal cancer patients.

BACKGROUND & AIM: Immune-modulating nutritional formula containing arginine, omega-3 fatty acids and nucleotides has been demonstrated to decrease complications and length of stay in surgical patients. This study aims at assessing the impact of immune-modulating formula on hospital costs in gastrointestinal cancer surgical patients in Switzerland. METHOD: Based on a previously published meta-analysis, the relative risks of overall and infectious complications with immune-modulating versus standard nutrition formula were computed. Swiss hospital costs of patients undergoing gastrointestinal cancer surgery were retrieved. A method was developed to compute the patients' severity level, not taking into account the complications from the surgery. Incremental costs of complications were computed for both treatment groups, and sensitivity analyses were carried out. RESULTS: Relative risk of complications with pre-, peri- and post-operative use of immune-modulating formula was 0.69 (95%CI 0.58-0.83), 0.62 (95%CI 0.53-0.73) and 0.73 (95%CI 0.35-0.96) respectively. The estimated average contribution of complications to the cost of stay was CHF 14,949 (euro10,901) per patient (95%CI 10,712-19,186), independently of case's severity. Based on this cost, immune-modulating nutritional support decreased costs of hospital stay by CHF 1638 to CHF 2488 per patient (euro1195-euro1814). Net hospital savings were present for baseline complications rates as low as 5%. CONCLUSION: Immune-modulating nutritional solution is a cost-saving intervention in gastrointestinal cancer patients. The additional cost of immune-modulating formula are more than offset by savings associated with decreased treatment of complications.

Cost-utility analysis of a three-month exercise programme vs usual care following multidisciplinary rehabilitation for chronic low back pain.

OBJECTIVE: To assess the cost-utility of an exercise programme vs usual care after functional multidisciplinary rehabilitation in patients with chronic low back pain. DESIGN: Cost-utility analysis alongside a randomized controlled trial. SUBJECTS/PATIENTS: A total of 105 patients with chronic low back pain. METHODS: Chronic low back pain patients completing a 3-week functional multidisciplinary rehabilitation were randomized to either a 3-month exercise programme (n = 56) or usual care (n = 49). The exercise programme consisted of 24 training sessions during 12 weeks. At the end of functional multidisciplinary rehabilitation and at 1-year follow-up quality of life was measured with the SF-36 questionnaire, converted into utilities and transformed into quality--adjusted life years. Direct and indirect monthly costs were measured using cost diaries. The incremental cost-effectiveness ratio was calculated as the incremental cost of the exercise programme divided by the difference in quality-adjusted life years between both groups. RESULTS: Quality of life improved significantly at 1-year follow-up in both groups. Similarly, both groups significantly reduced total monthly costs over time. No significant difference was observed between groups. The incremental cost-effectiveness ratio was 79,270 euros. CONCLUSION: Adding an exercise programme after functional multidisciplinary rehabilitation compared with usual care does not offer significant long-term benefits in quality of life and direct and indirect costs.

Whole-body vibration training: metabolic cost of synchronous, side-alternating or no vibrations.

Whole-body vibration training improves strength and can increase maximal oxygen consumption ([·V]O(2max)). No study has compared the metabolic demand of synchronous and side-alternating whole-body vibration. We measured [·V]O₂ and heart rate during a typical synchronous or side-alternating whole-body vibration session in 10 young female sedentary participants. The 20-min session consisted of three sets of six 45-s exercises, with 15 s recovery between exercises. Three conditions were randomly tested on separate days: synchronous at 35 Hz and 4 mm amplitude, side-alternating at 26 Hz and 7.5 mm amplitude (peak acceleration matched at 20 g in both vibration conditions), and no vibrations. Mean [·V]O₂ (expressed as %[·V]O(2max)) did not differ between conditions: 29.7 ± 4.2%, 32.4 ± 6.5%, and 28.7 ± 6.7% for synchronous, side-alternating, and no vibrations respectively (P = 0.103). Mean heart rate (% maximal heart rate) was 65.6 ± 7.3%, 69.8 ± 7.9%, and 64.7 ± 5.6% for synchronous, side-alternating, and no vibrations respectively, with the side-alternating vibrations being significantly higher (P = 0.019). When analysing changes over exercise sessions, mean [·V]O₂ was higher for side-alternating (P < 0.001) than for synchronous and no vibrations. In conclusion, side-alternating whole-body vibration elicits higher heart rate responses than synchronous or no vibrations, and could elevate [·V]O₂, provided the session lasts more than 20 min.