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

Problema-experiencia para construir un modelo redox

En las aulas universitarias, existe una separación muy común entre “teoría”, “trabajo experimental” y “problemas”. En este trabajo se analizan los resultados de una experiencia que busca integrar esas tres actividades. En la Facultad de Ciencias Veterinarias de la UNCPBA, en Tandil (Argentina), a un grupo de alumnos de primer año, se les propuso un problema a investigar. Debían armar un diseño experimental, ejecutarlo, comparar resultados, extraer inferencias de un hecho empírico, y aplicar conceptos de óxido-reducción. Al comenzar la actividad se percibe el desconcierto de los estudiantes frente a esta problemática inusual para ellos (diseñar un trabajo experimental), pero luego la realizan en forma cooperativa y con entusiasmo

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

Bioelectrical impedance phase angle in clinical practice: implications for prognosis in stage IIIB and IV non-small cell lung cancer

<p>Abstract</p> <p>Background</p> <p>A frequent manifestation of advanced lung cancer is malnutrition, timely identification and treatment of which can lead to improved patient outcomes. Bioelectrical impedance analysis (BIA) is an easy-to-use and non-invasive technique to evaluate changes in body composition and nutritional status. We investigated the prognostic role of BIA-derived phase angle in advanced non-small cell lung cancer (NSCLC).</p> <p>Methods</p> <p>A case series of 165 stages IIIB and IV NSCLC patients treated at our center. The Kaplan Meier method was used to calculate survival. Cox proportional hazard models were constructed to evaluate the prognostic effect of phase angle, independent of stage at diagnosis and prior treatment history.</p> <p>Results</p> <p>93 were males and 72 females. 61 had stage IIIB disease at diagnosis while 104 had stage IV. The median phase angle was 5.3 degrees (range = 2.9 – 8). Patients with phase angle <= 5.3 had a median survival of 7.6 months (95% CI: 4.7 to 9.5; n = 81), while those with > 5.3 had 12.4 months (95% CI: 10.5 to 18.7; n = 84); (p = 0.02). After adjusting for age, stage at diagnosis and prior treatment history we found that every one degree increase in phase angle was associated with a relative risk of 0.79 (95% CI: 0.64 to 0.97, P = 0.02).</p> <p>Conclusion</p> <p>We found BIA-derived phase angle to be an independent prognostic indicator in patients with stage IIIB and IV NSCLC. Nutritional interventions targeted at improving phase angle could potentially lead to an improved survival in patients with advanced NSCLC.</p

Bioelectrical impedance phase angle as a prognostic indicator in breast cancer

<p>Abstract</p> <p>Background</p> <p>Bioelectrical impedance analysis (BIA) is an easy-to-use, non-invasive, and reproducible technique to evaluate changes in body composition and nutritional status. Phase angle, determined by bioelectrical impedance analysis (BIA), detects changes in tissue electrical properties and has been hypothesized to be a marker of malnutrition. Since malnutrition can be found in patients with breast cancer, we investigated the prognostic role of phase angle in breast cancer.</p> <p>Methods</p> <p>We evaluated a case series of 259 histologically confirmed breast cancer patients treated at Cancer Treatment Centers of America. Kaplan Meier method was used to calculate survival. Cox proportional hazard models were constructed to evaluate the prognostic effect of phase angle independent of stage at diagnosis and prior treatment history. Survival was calculated as the time interval between the date of first patient visit to the hospital and the date of death from any cause or date of last contact/last known to be alive.</p> <p>Results</p> <p>Of 259 patients, 81 were newly diagnosed at our hospital while 178 had received prior treatment elsewhere. 56 had stage I disease at diagnosis, 110 had stage II, 46 had stage III and 34 had stage IV. The median age at diagnosis was 49 years (range 25 – 74 years). The median phase angle score was 5.6 (range = 1.5 – 8.9). Patients with phase angle <= 5.6 had a median survival of 23.1 months (95% CI: 14.2 to 31.9; n = 129), while those > 5.6 had 49.9 months (95% CI: 35.6 to 77.8; n = 130); the difference being statistically significant (p = 0.031). Multivariate Cox modeling, after adjusting for stage at diagnosis and prior treatment history found that every one unit increase in phase angle score was associated with a relative risk of 0.82 (95% CI: 0.68 to 0.99, P = 0.041). Stage at diagnosis (p = 0.006) and prior treatment history (p = 0.001) were also predictive of survival independent of each other and phase angle.</p> <p>Conclusion</p> <p>This study demonstrates that BIA-derived phase angle is an independent prognostic indicator in patients with breast cancer. Nutritional interventions targeted at improving phase angle could potentially lead to an improved survival in patients with breast cancer.</p

Understanding the olfactory role in post-COVID cognitive and neuropsychiatric manifestations

IntroductionOlfactory dysfunction (OD) is frequent after SARS-CoV-2 infection. The aim of this study was to examine if long-term OD is common in post-COVID condition, and the relationship between olfaction, cognition, neuropsychiatric symptoms, and disease duration in these patients.MethodsThis study included 121 participants with post-COVID condition and 51 healthy controls (HC). A comprehensive neuropsychological and neuropsychiatric assessment was conducted, encompassing various domains, including general cognition, processing speed, verbal fluency, attention, verbal memory, visual memory, visuoconstructive ability, visuospatial ability, abstraction, executive functions, anxious-depressive symptoms, general health perception, fatigue level, sleep quality, and olfaction. Statistical analyses were carried out to understand the relationship of OD with cognition, and its role as moderator variable.ResultsIn total, 25% of the post-covid patients had a reduced smell capacity, while only 9.3% of HC presented OD. Post-COVID patients had statistically significantly worse cognitive performance and clinical status than HC. Verbal fluency (AUC = 0.85, p &lt; 0.001), and attention (AUC = 0.82, p &lt; 0.001) were the variables that best discriminate between groups. OD seemed to be a moderator between fatigue and cognition, and between disease duration and attention (β = −0.04; p = 0.014).DiscussionThe study highlights marked cognitive and neuropsychiatric sequelae in individuals post-COVID relative to HC. Olfactory impairment exhibits correlations with both cognitive performance and general health. Olfaction emerges as a potential prognostic marker owing to its moderating influence on disease severity indicators

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