Optimal dividend strategies for two collaborating insurance companies

We consider a two-dimensional optimal dividend problem in the context of two insurance companies with compound Poisson surplus processes, who collaborate by paying each other's deficit when possible. We solve the stochastic control problem of maximizing the weighted sum of expected discounted dividend payments (among all admissible dividend strategies) until ruin of both companies, by extending results of univariate optimal control theory. In the case that the dividends paid by the two companies are equally weighted, the value function of this problem compares favorably with the one of merging the two companies completely. We identify this optimal value function as the smallest viscosity supersolution of the respective Hamilton-Jacobi-Bellman equation and provide an iterative approach to approximate it numerically. Curve strategies are identified as the natural analogue of barrier strategies in this two-dimensional context. A numerical example is given for which such a curve strategy is indeed optimal among all admissible dividend strategies, and for which this collaboration mechanism also outperforms the suitably weighted optimal dividend strategies of the two stand-alone companies

Experience of the cleft lip and palate clinic at the hospital general de México 2017-2023

Background: The care of cleft lip and palate patients at the general hospital of Mexico has nearly 70 years of experience. Methods: An observational study of a 7-year cohort of resolved cases of cleft lip and palate by the plastic and reconstructive surgery service of the general hospital of Mexico (2017-2023) was conducted. Results: The 121 patients were recorded, with 47 palatoplasties, 44 primary cheiloplasties, 24 secondary cheiloplasties, and 11 veloplasties performed. All patients are evaluated by a multidisciplinary team composed of plastic surgery, dentistry, clinical nutrition, speech therapy, audiology, genetics, and psychology to determine a comprehensive treatment plan. Conclusions: The data reported by the cohort in this work aligns with international reports. The frequency of cases decreased due to the COVID-19 pandemic, but has increased in recent years

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

Toxic Metals (Pb and Cd) and Their Respective Antagonists (Ca and Zn) in Infant Formulas and Milk Marketed in Brasilia, Brazil

In non-ideal scenarios involving partial or non-breastfeeding, cow’s milk-based dairy products are mainstream in infant feeding. Therefore, it is important to study the concentrations of potentially neurotoxic contaminants (Pb and Cd) and their respective counteracting elements (Ca and Zn) in infant dairy products. Fifty-five brands of infant formulas and milk sold in Brasilia, Brazil were analyzed. The dairy products came from areas in the central-west (26%), southeast (29%) and south of Brazil (36%) extending as far as Argentina (7%) and the Netherlands (2%). For toxic Pb and Cd, median concentrations in powdered samples were 0.109 mg/kg and 0.033 mg/kg, respectively; in fluid samples median Pb concentration was 0.084 mg/kg, but median Cd concentration was below the limit of detection and overall values were below reference safety levels. However, 62% of these samples presented higher Pb concentration values than those established by FAO/WHO. Although the inverse correlation between Cd and Zn (Spearman r = −0.116; P = 0.590) was not statistically significant, the positive correlation between Ca and Pb was (Spearman r = 0.619; P < 0.0001). Additionally, there was a significant correlation between Pb and Cd. Furthermore, the study also revealed that provision of the essential trace element Zn in infant formulas can provide adequate amounts of the recommended daily requirements. Infant formulas and milk sold for consumption by infants and children can be an efficient tool to monitor neurotoxic metal risk exposure among young children

Optimal dividend payout in random discrete time

Assume that the surplus process of an insurance company is described by a general Lévy process and that possible dividend pay-outs to shareholders are restricted to random discrete times which are determined by an independent renewal process. Under this setting we show that the optimal dividend pay-out policy is a band-policy. If the renewal process is a Poisson process, it is further shown that for Cramér–Lundberg risk processes with exponential claim sizes and its diffusion limit the optimal policy collapses to a barrier-policy. Finally, a numerical example is given for which the optimal bands can be calculated explicitly. The random observation procedure studied in this paper also allows for an interpretation in terms of a random walk model with a certain type of random discounting

Optimal dividends under a drawdown constraint and a curious square-root rule

In this paper we address the problem of optimal dividend payout strategies from a surplus process governed by Brownian motion with drift under a drawdown constraint, i.e. the dividend rate can never decrease below a given fraction a of its historical maximum. We solve the resulting two-dimensional optimal control problem and identify the value function as the unique viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation. We then derive su cient conditions under which a two-curve strategy is optimal, and show how to determine its concrete form using calculus of variations. We establish a smooth-pasting principle and show how it can be used to prove the optimality of two-curve strategies for su ciently large initial and maximum dividend rate. We also give a number of numerical illustrations in which the optimality of the two-curve strategy can be established for instances with smaller values of the maximum dividend rate, and the concrete form of the curves can be determined. One observes that the resulting drawdown strategies nicely interpolate between the solution for the classical unconstrained dividend problem and the one for a ratcheting constraint as recently studied in [1]. When the maximum allowed dividend rate tends to in nity, we show a surprisingly simple and somewhat intriguing limit result in terms of the parameter a for the surplus level on from which, for su ciently large current dividend rate, a take-the-money-and-run strategy is optimal in the presence of the drawdown constraint.Este documento es una versión del artículo publicado en Finance Stochastics 27, 341–400 (2023