The optimal dividend barrier in the Gamma-Omega model

In the traditional actuarial risk model, if the surplus is negative, the company is ruined and has to go out of business. In this paper we distinguish between ruin (negative surplus) and bankruptcy (going out of business), where the probability of bankruptcy is a function of the level of negative surplus. The idea for this notion of bankruptcy comes from the observation that in some industries, companies can continue doing business even though they are technically ruined. Assuming that dividends can only be paid with a certain probability at each point of time, we derive closed-form formulas for the expected discounted dividends until bankruptcy under a barrier strategy. Subsequently, the optimal barrier is determined, and several explicit identities for the optimal value are found. The surplus process of the company is modeled by a Wiener process (Brownian motion).

When "enough" is not enough: new perspectives on optimal methadone maintenance dose.

Some methadone maintenance treatment (MMT) programs prescribe inadequate daily methadone doses. Patients complain of withdrawal symptoms and continue illicit opioid use, yet practitioners are reluctant to increase doses above certain arbitrary thresholds. Serum methadone levels (SMLs) may guide practitioners dosing decisions, especially for those patients who have low SMLs despite higher methadone doses. Such variation is due in part to the complexities of methadone metabolism. The medication itself is a racemic (50:50) mixture of 2 enantiomers: an active "R" form and an essentially inactive "S" form. Methadone is metabolized primarily in the liver, by up to five cytochrome P450 isoforms, and individual differences in enzyme activity help explain wide ranges of active R-enantiomer concentrations in patients given identical doses of racemic methadone. Most clinical research studies have used methadone doses of less than 100 mg/day [d] and have not reported corresponding SMLs. New research suggests that doses ranging from 120 mg/d to more than 700 mg/d, with correspondingly higher SMLs, may be optimal for many patients. Each patient presents a unique clinical challenge, and there is no way of prescribing a single best methadone dose to achieve a specific blood level as a "gold standard" for all patients. Clinical signs and patient-reported symptoms of abstinence syndrome, and continuing illicit opioid use, are effective indicators of dose inadequacy. There does not appear to be a maximum daily dose limit when determining what is adequately "enough" methadone in MMT.

Population density and optimal body size.

The population density of an organism is one of the main aspects of its environment, and shoud therefore strongly influence its adaptive strategy. The r/K theory, based on the logistic model, was developed to formalize this influence. K-selectioon is classically thought to favour large body sizes. This prediction, however, cannot be directly derived from the logistic model: some auxiliary hypotheses are therefor implicit. These are to be made explicit if the theory is to be tested. An alternative approach, based on the Euler-Lotka equation, shows that density itself is irrelevant, but that the relative effect of density on adult and juvenile features is crucial. For instance, increasing population will select for a smaller body size if the density affects mainly juvenile growth and/or survival. In this case, density shoud indeed favour large body sizes. The theory appears nevertheless inconsistent, since a probable consequence of increasing body size will be a decrease in the carrying capacity

Erste Resultate der HOT-Studie in der Schweiz. [Initial results of the HOT-study in Switzerland (hypertension optimal treatment)]

The HOT study (hypertension-optimal treatment) is an international clinical study on primary prevention of cardiovascular events in 19,193 hypertensive patients worldwide. It aims at the recognition of the optimal diastolic blood pressure value (< 90, < 85 or < 80 mmHg?) in order to maximize the possible benefit of an antihypertensive therapy. In addition, the HOT study investigates whether low doses of aspirin (75 mg/day) are able to reduce the occurrence of severe cardiovascular events. In Switzerland a total of 797 patients have been enrolled in the study. Antihypertensive therapy was initiated with felodipine = Plendil (5 mg/day). This vasoelective calcium antagonist could reduce diastolic blood pressure values to < 90 or < 80 mg/Hg, respectively, in one of two or one of three patients within the first three months. In nine or six patients, respectively out of ten a reduction of diastolic blood pressure values to < 90 or < 80 mmHg was reached within one year by combination of felodipine with other antihypertensive drugs (ACE inhibitors, beta blockers and diuretics).

Ispol'zovanie metodov teorii vosstanovleniia v modeliakh optimal'nogo dobyvaniia pishchi [Restoration theory in models of optimal feeding behavior]

The method of stochastic dynamic programming is widely used in ecology of behavior, but has some imperfections because of use of temporal limits. The authors presented an alternative approach based on the methods of the theory of restoration. Suggested method uses cumulative energy reserves per time unit as a criterium, that leads to stationary cycles in the area of states. This approach allows to study the optimal feeding by analytic methods.

Optimal activation of tumor-reactive T cells by selected antigenic peptide analogues.

Many mechanisms have been proposed to explain why immune responses against human tumor antigens are generally ineffective. For example, tumor cells have been shown to develop active immune evasion mechanisms. Another possibility is that tumor antigens are unable to optimally stimulate tumor-specific T cells. In this study we have used HLA-A2/Melan-A peptide tetramers to directly isolate antigen-specific CD8(+) T cells from tumor-infiltrated lymph nodes. This allowed us to quantify the activation requirements of a representative polyclonal yet monospecific tumor-reactive T cell population. The results obtained from quantitative assays of intracellular Ca(2+) mobilization, TCR down-regulation, cytokine production and induction of effector cell differentiation indicate that the naturally produced Melan-A peptides are weak agonists and are clearly suboptimal for T cell activation. In contrast, optimal T cell activation was obtained by stimulation with recently defined peptide analogues. These findings provide a molecular basis for the low immunogenicity of tumor cells and suggest that patient immunization with full agonist peptide analogues may be essential for stimulation and maintenance of anti-tumor T cell responses in vivo.

Optimal fiscal policy in overlapping generations models

[eng] This paper provides, from a theoretical and quantitative point of view, an explanation of why taxes on capital returns are high (around 35%) by analyzing the optimal fiscal policy in an economy with intergenerational redistribution. For this purpose, the government is modeled explicitly and can choose (and commit to) an optimal tax policy in order to maximize society's welfare. In an infinitely lived economy with heterogeneous agents, the long run optimal capital tax is zero. If heterogeneity is due to the existence of overlapping generations, this result in general is no longer true. I provide sufficient conditions for zero capital and labor taxes, and show that a general class of preferences, commonly used on the macro and public finance literature, violate these conditions. For a version of the model, calibrated to the US economy, the main results are: first, if the government is restricted to a set of instruments, the observed fiscal policy cannot be disregarded as sub optimal and capital taxes are positive and quantitatively relevant. Second, if the government can use age specific taxes for each generation, then the age profile capital tax pattern implies subsidizing asset returns of the younger generations and taxing at higher rates the asset returns of the older ones.

Interiority of the optimal population growth rate with endogenous fertility

This paper analyzes the issue of the interiority of the optimal population growth rate in a two-period overlapping generations model with endogenous fertility. Using Cobb-Douglas utility and production functions, we show that the introduction of a cost of raising children allows for the possibility of the existence of an interior global maximum in the planner¿s problem, contrary to the exogenous fertility case

Optimal generalized quantum measurements for arbitrary spin systems

Positive-operator-valued measurements on a finite number of N identically prepared systems of arbitrary spin J are discussed. Pure states are characterized in terms of Bloch-like vectors restricted by a SU(2J+1) covariant constraint. This representation allows for a simple description of the equations to be fulfilled by optimal measurements. We explicitly find the minimal positive-operator-valued measurement for the N=2 case, a rigorous bound for N=3, and set up the analysis for arbitrary N.

Optimal Usage of De-Icing Chemicals when Scraping Ice, November 2003

One of the challenges that faces the winter maintainer is how much chemical to apply to the road under given conditions. Insufficient chemical can lead to the road surface becoming slick, and the road thus becoming unsafe. In all likelihood, additional applications will have to be made, requiring additional effort and use of resources. However, too much chemical can also be bad. While an excess of chemical will ensure (in most circumstances) that a safe road condition is achieved, it may also result in a substantial waste of chemical (with associated costs for this waste) and in ancillary damage to the road itself and to the surrounding environment. Ideally, one should apply what might be termed the “goldilocks” amount of chemical to the road: Not too much, and not too little, but just right. Of course the reality of winter maintenance makes achieving the “goldilocks” application rate somewhat of a fairy tale. In the midst of a severe storm, when conditions are poor and getting worse, the last thing on a plow operator’s mind is a minute adjustment in the amount of chemical being applied to the road. However, there may be considerable benefit and substantial savings to be achieved if chemical applications can be optimized to some degree, so that wastage is minimized without compromising safety. The goal of this study was to begin to develop such information through a series of laboratory studies in which the force needed to scrape ice from concrete blocks was measured, under a variety of chemical application conditions.

Optimal growth strategies when mortality and production rates are size-dependent

Pontryagin's maximum principle from optimal control theory is used to find the optimal allocation of energy between growth and reproduction when lifespan may be finite and the trade-off between growth and reproduction is linear. Analyses of the optimal allocation problem to date have generally yielded bang-bang solutions, i.e. determinate growth: life-histories in which growth is followed by reproduction, with no intermediate phase of simultaneous reproduction and growth. Here we show that an intermediate strategy (indeterminate growth) can be selected for if the rates of production and mortality either both increase or both decrease with increasing body size, this arises as a singular solution to the problem. Our conclusion is that indeterminate growth is optimal in more cases than was previously realized. The relevance of our results to natural situations is discussed.

Universality of optimal measurements

We present optimal and minimal measurements on identical copies of an unknown state of a quantum bit when the quality of measuring strategies is quantified with the gain of information (Kullback-or mutual information-of probability distributions). We also show that the maximal gain of information occurs, among isotropic priors, when the state is known to be pure. Universality of optimal measurements follows from our results: using the fidelity or the gain of information, two different figures of merits, leads to exactly the same conclusions for isotropic distributions. We finally investigate the optimal capacity of N copies of an unknown state as a quantum channel of information.