The Effect of a Threshold Proportional Reinsurance Strategy on Ruin Probabilities

In the context of a compound Poisson risk model, we define a threshold proportional reinsurance strategy: A retention level k1 is applied whenever the reserves are less than a determinate threshold b, and a retention level k2 is applied in the other case. We obtain the integro-differential equation for the Gerber-Shiu function (defined in Gerber and Shiu (1998)) in this model, which allows us to obtain the expressions for ruin probability and Laplace transforms of time of ruin for several distributions of the claim sizes. Finally, we present some numerical results.time of ruin, threshold proportional reinsurance strategy, ruin probability, gerber-shiu function

Time of ruin in a risk model with generalized Erlang (n) interclaim times and a constant dividend barrier

In this paper we analyze the time of ruin in a risk process with the interclaim times being Erlang(n) distributed and a constant dividend barrier. We obtain an integro-differential equation for the Laplace Transform of the time of ruin. Explicit solutions for the moments of the time of ruin are presented when the individual claim amounts have a distribution with rational Laplace transform. Finally, some numerical results and a compare son with the classical risk model, with interclaim times following an exponential distribution, are given.risk theory, constant dividend barrier, laplace transform, time of ruin, generalized erlang (n) distribution

Discrete analysis of dividend payments in a non-life insurance portfolio

The process of free reserves in a non-life insurance portfolio as defined in the classical model of risk theory is modified by the introduction of dividend policies that set maximum levels for the accumulation of reserves. The first part of the work formulates the quantification of the dividend payments via the expectation of their current value under different hypotheses. The second part presents a solution based on a system of linear equations for discrete dividend payments in the case of a constant dividend barrier, illustrated by solving a specific case.dividend policies, expected present value

La probabilidad de supervivencia en un modelo con reaseguro proporcional de umbral

In this paper we present a new reinsurance strategy, called threshold strategy, that has a different behaviour depending on the reserves. Whenever the reserves are less than a certain level, the portfolio manager decides to apply a proportional reinsurance. If the reserves are greater than b, it is considered that the level of solvency is enough, and then the decision is not ceding any risk. The study of the effect of the introduction of the threshold reinsurance on the survival probability, and the comparison with the proportional reinsurance and the option of not reinsuring, allows us to find equivalent strategies of reinsurance from the solvency point of view.survival probability, proportional reinsurance, threshold reinsurance, risk theory

Politicas de dividendos y probabilidad de ruina

In this paper we introduce different kinds of dividend barriers in the classical model ruin theory. We study the influence of barrier strategy on ruin probability. A method based on renewal equations [Grandell (1991)], alternative to differential argument [Gerber (1975)], is used to get the partial differential equations to solve survival probabilities. Finally we calculate and compare the survival probabilities using the linear and the parabolic dividend barrier, with help of simulation.ruin, survival probability, theory, dividend barriers

Optimal Dividend Strategies: Some Economic Interpretations for the Constant Barrier Case

We consider the surplus process of a non-life insurance portfolio with a dividend component represented by a constant dividend barrier strategy. The optimal dividend barrier is known when individual claim amounts follow an exponential distribution. This result for the optimal dividend barrier is used to develop combinations of the levels of the insurer\u27s initial surplus and of the barrier which, under certain economic and financial criteria, can be regarded as optimal

Evaluation of Nutritional Practices in the Critical Care patient (The ENPIC study) : Does nutrition really affect ICU mortality?

The importance of artificial nutritional therapy is underrecognized, typically being considered an adjunctive rather than a primary therapy. We aimed to evaluate the influence of nutritional therapy on mortality in critically ill patients. Methods: This multicenter prospective observational study included adult patients needing artificial nutritional therapy for >48 h if they stayed in one of 38 participating intensive care units for ≥72 h between April and July 2018. Demographic data, comorbidities, diagnoses, nutritional status and therapy (type and details for ≤14 days), and outcomes were registered in a database. Confounders such as disease severity, patient type (e.g., medical, surgical or trauma), and type and duration of nutritional therapy were also included in a multivariate analysis, and hazard ratios (HRs) and 95% confidence intervals (95%CIs) were reported. We included 639 patients among whom 448 (70.1%) and 191 (29.9%) received enteral and parenteral nutrition, respectively. Mortality was 25.6%, with non-survivors having the following characteristics: older age; more comorbidities; higher Sequential Organ Failure Assessment (SOFA) scores (6.6 ± 3.3 vs 8.4 ± 3.7; P < 0.001); greater nutritional risk (Nutrition Risk in the Critically Ill [NUTRIC] score: 3.8 ± 2.1 vs 5.2 ± 1.7; P < 0.001); more vasopressor requirements (70.4% vs 83.5%; P=0.001); and more renal replacement therapy (12.2% vs 23.2%; P=0.001). Multivariate analysis showed that older age (HR: 1.023; 95% CI: 1.008-1.038; P=0.003), higher SOFA score (HR: 1.096; 95% CI: 1.036-1.160; P=0.001), higher NUTRIC score (HR: 1.136; 95% CI: 1.025-1.259; P=0.015), requiring parenteral nutrition after starting enteral nutrition (HR: 2.368; 95% CI: 1.168-4.798; P=0.017), and a higher mean Kcal/Kg/day intake (HR: 1.057; 95% CI: 1.015-1.101; P=0.008) were associated with mortality. By contrast, a higher mean protein intake protected against mortality (HR: 0.507; 95% CI: 0.263-0.977; P=0.042). Old age, higher organ failure scores, and greater nutritional risk appear to be associated with higher mortality. Patients who need parenteral nutrition after starting enteral nutrition may represent a high-risk subgroup for mortality due to illness severity and problems receiving appropriate nutritional therapy. Mean calorie and protein delivery also appeared to influence outcomes. ClinicaTrials.gov NCT: 03634943