Constraint Effective Potential of the Staggered Magnetization in an Antiferromagnet

We employ an improved estimator to calculate the constraint effective potential of the staggered magnetization in the spin $\tfrac{1}{2}$ quantum Heisenberg model using a loop-cluster algorithm. The first and second moment of the probability distribution of the staggered magnetization are in excellent agreement with the predictions of the systematic low-energy magnon effective field theory. We also compare the Monte Carlo data with the universal shape of the constraint effective potential of the staggered magnetization and study its approach to the convex effective potential in the infinite volume limit. In this way the higher-order low-energy parameter $k_0$ is determined from a fit to the numerical data

A Remark on the Principle of Zero Utility

Let u(x) be a utility function, i.e., a function with u′(x)>0, u″(x)<0 for all x. If S is a risk to be insured (a random variable), the premium P = P(x) is obtained as the solution of the equation which is the condition that the premium is fair in terms of utility. It is clear that an affine transformation of u generates the same principle of premium calculation. To avoid this ambiguity, one can standardize the utility function in the sense that for an arbitrarily chosen point y. Alternatively, one can consider the risk aversion which is the same for all affine transformations of a utility function. Given the risk aversion r(x), the standardized utility function can be retrieved from the formula It is easily verified that this expression satisfies (2) and (3). The following lemma states that the greater the risk aversion the greater the premium, a result that does not surpris

A Stochastic Volatility Model With Realized Measures for Option Pricing

Based on the fact that realized measures of volatility are affected by measurement errors, we introduce a new family of discrete-time stochastic volatility models having two measurement equations relating both observed returns and realized measures to the latent conditional variance. A semi-analytical option pricing framework is developed for this class of models. In addition, we provide analytical filtering and smoothing recursions for the basic specification of the model, and an effective MCMC algorithm for its richer variants. The empirical analysis shows the effectiveness of filtering and smoothing realized measures in inflating the latent volatility persistence—the crucial parameter in pricing Standard and Poor’s 500 Index options

Optimal Dividends in the Dual Model with Diffusion

In the dual model, the surplus of a company is a Lévy process with sample paths that are skip-free downwards. In this paper, the aggregate gains process is the sum of a shifted compound Poisson process and an independent Wiener process. By means of Laplace transforms, it is shown how the expectation of the discounted dividends until ruin can be calculated, if a barrier strategy is applied, and how the optimal dividend barrier can be determined. Conditions for optimality are discussed and several numerical illustrations are given. Furthermore, a family of models is analysed where the individual gain amount distribution is rescaled and compensated by a change of the Poisson paramete

Three Methods to Calculate the Probability of Ruin

The first method, essentially due to GOOVAERTS and DE VYLDER, uses the connection between the probability of ruin and the maximal aggregate loss random variable, and the fact that the latter has a compound geometric distribution. For the second method, the claim amount distribution is supposed to be a combination of exponential or translated exponential distributions. Then the probability of ruin can be calculated in a transparent fashion; the main problem is to determine the nontrivial roots of the equation that defines the adjustment coefficient. For the third method one observes that the probability, of ruin is related to the stationary distribution of a certain associated process. Thus it can be determined by a single simulation of the latter. For the second and third methods the assumption of only proper (positive) claims is not neede

Microscopic Model versus Systematic Low-Energy Effective Field Theory for a Doped Quantum Ferromagnet

We consider a microscopic model for a doped quantum ferromagnet as a test case for the systematic low-energy effective field theory for magnons and holes, which is constructed in complete analogy to the case of quantum antiferromagnets. In contrast to antiferromagnets, for which the effective field theory approach can be tested only numerically, in the ferromagnetic case both the microscopic and the effective theory can be solved analytically. In this way the low-energy parameters of the effective theory are determined exactly by matching to the underlying microscopic model. The low-energy behavior at half-filling as well as in the single- and two-hole sectors is described exactly by the systematic low-energy effective field theory. In particular, for weakly bound two-hole states the effective field theory even works beyond perturbation theory. This lends strong support to the quantitative success of the systematic low-energy effective field theory method not only in the ferromagnetic but also in the physically most interesting antiferromagnetic case.Comment: 34 pages, 1 figur

In-vivo assessment of in-vitro killing patterns of Pseudomonas aeruginosa

Time-kill curves of Pseudomonas aeruginosa exposed to gentamicin or ticarcilhn in vitro were correlated with time-kill curves obtained with various dosage schedules of the same study drugs in granulocytopenic mice. An instantaneous, fast and drug-dependent killing pattern was found in vitro with gentamicin. This pattern corresponded to bacterial killing in vivo which was clearly dependent on peak drug levels. In contrast, slow bacterial killing with little relationship to concentration was found in vitro with ticarcilhn and proved to correlate with an antibacterial effect in vivo seen at trough levels. We conclude that in-vitro time-kill curves of antimicrobial agents may be predictive for optimizing dosage regimens in viv

The MUCHFUSS photometric campaign

Hot subdwarfs (sdO/Bs) are the helium-burning cores of red giants, which lost almost all of their hydrogen envelopes. This mass loss is often triggered by common envelope interactions with close stellar or even substellar companions. Cool companions like late-type stars or brown dwarfs are detectable via characteristic light curve variations like reflection effects and often also eclipses. To search for such objects we obtained multi-band light curves of 26 close sdO/B binary candidates from the MUCHFUSS project with the BUSCA instrument. We discovered a new eclipsing reflection effect system ($P=0.168938$~d) with a low-mass M dwarf companion ($0.116 M_{\rm \odot}$). Three more reflection effect binaries found in the course of the campaign were already published, two of them are eclipsing systems, in one system only showing the reflection effect but no eclipses the sdB primary is found to be pulsating. Amongst the targets without reflection effect a new long-period sdB pulsator was discovered and irregular light variations were found in two sdO stars. The found light variations allowed us to constrain the fraction of reflection effect binaries and the substellar companion fraction around sdB stars. The minimum fraction of reflection effect systems amongst the close sdB binaries might be greater than 15\% and the fraction of close substellar companions in sdB binaries might be as high as $8.0\%$. This would result in a close substellar companion fraction to sdB stars of about 3\%. This fraction is much higher than the fraction of brown dwarfs around possible progenitor systems, which are solar-type stars with substellar companions around 1 AU, as well as close binary white dwarfs with brown dwarf companions. This might be a hint that common envelope interactions with substellar objects are preferentially followed by a hot subdwarf phase.Comment: accepted for A&

Martingale Approach to Pricing Perpetual American Options

The method of Esscher transforms is a tool for valuing options on a stock, if the logarithm of the stock price is governed by a stochastic process with stationary and independent increments. The price of a derivative security is calculated as the expectation, with respect to the risk-neutral Esscher measure, of the discounted payoffs. Applying the optional sampling theorem we derive a simple, yet general formula for the price of a perpetual American put option on a stock whose downward movements are skip-free. Similarly, we obtain a formula for the price of a perpetual American call option on a stock whose upward movements are skip-free. Under the classical assumption that the stock price is a geometric Brownian motion, the general perpetual American contingent claim is analysed, and formulas for the perpetual down-and-out call option and Russian option are obtained. The martingale approach avoids the use of differential equations and provides additional insight. We also explain the relationship between Samuelson's high contact condition and the first order condition for optimalit