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We investigate a new basic model for asset pricing, the hyperbolic model, which allows an almost perfect statistical fit of stock return data. After a brief introduction into the theory supported by an appendix we use also secondary market data to compare the hyperbolic model to the classical Black-Scholes model. We study implicit volatilities, the smile effect and the pricing performance. Exploiting the full power of the hyperbolic model, we construct an option value process from a statistical point of view by estimating the implicit risk-neutral density function from option data. Finally we present some new valueat -risk calculations leading to new perspectives to cope with model risk. I Introduction There is little doubt that the Black-Scholes model has become the standard in the finance industry and is applied on a large scale in everyday trading operations. On the other side its deficiencies have become a standard topic in research. Given the vast literature where refinements a...

Present and permanent address: Physik-Department der TU Munchen Exploiting local stability we show what neuronal characteristics are essential to ensure that coherent oscillations are asymptotically stable in a spatially homogeneous network of spiking neurons. Under standard conditions, a necessary and in the limit of a large number of interacting neighbors also sufficient condition is that the postsynaptic potential is increasing in time as the neurons fire. If the postsynaptic potential is decreasing, oscillations are bound to be unstable. This is a kind of locking theorem and boils down to a subtle interplay of axonal delays, postsynaptic potentials, and refractory behavior. The theorem also allows for mixtures of excitatory and inhibitory interactions. On the basis of the locking theorem we present a simple geometric method to verify existence and local stability of a coherent oscillation. 2 1

. We consider simple random walk on the family tree T of a nondegenerate supercritical Galton-Watson branching process and show that the resulting harmonic measure has a.s. strictly smaller Hausdorff dimension than that of the whole boundary of T . Concretely, this implies that an exponentially small fraction of the nth level of T carries most of the harmonic measure. First order asymptotics for the rate of escape, Green function and the Avez entropy of the random walk are also determined. Ergodic theory of the shift on the space of random walk paths on trees is the main tool; the key observation is that iterating the transformation induced from this shift to the subset of "exit points" yields a nonintersecting path sampled from harmonic measure. x1. Introduction. Consider a supercritical Galton-Watson branching process with generating function f(s) = P 1 k=0 p k s k , i.e., each individual has k offspring with probability p k , and m := f 0 (1) ? 1. Started with a single prog...

This paper explores how Bayes-rational individuals learn sequentially from the discrete actions of others. Unlike earlier informational herding papers, we admit heterogeneous preferences. Not only may type-specific `herds' eventually arise, but a new robust possibility emerges: confounded learning. Beliefs may converge to a limit point where history oers no decisive lessons for anyone, and each type's actions forever nontrivially split between two actions. To verify that our identied limit outcomes do arise, we exploit the Markov-martingale character of beliefs. Learning dynamics are stochastically stable near a fixed point in many Bayesian learning models like this one.

Many biological and biochemical measurements, e.g. the "fitness" of a particular genome, or the binding affinity to a particular substrate, can be treated as a "fitness landscape", an assignment of numerical values to points in sequence space (or some other configuration space). As an alternative to the enormous amount of data required to completely describe such a landscape, we propose a statistical characterization, based on the properties of a random walk through the landscape, and, more specifically, its autocorrelation function. Under assumptions roughly satisfied by two classes of simple model landscapes (the N-k model and the p-spin model) and by the landscape of estimated free energies of RNA secondary structures, this autocorrelation function, along with the mean and variance of individual points and the size of the landscape, completely characterize it. Having noted that these and other landscapes of estimated replication and degradation rates all have a well defined correlat...

This paper describes an efficient technique for estimating, via simulation, the probability of buffer overows in a queueing model that arises in the analysis of ATM (Asynchronous Transfer Mode) communication switches. There are multiple streams of (autocorrelated) traffic feeding the switch that has a buffer of finite capacity. Each stream is designated as either being of high or low priority. When the queue length reaches a certain threshold, only high priority packets are admitted to the switch's buffer. The problem is to estimate the loss rate of high priority packets. An asymptotically optimal importance sampling approach is developed for this rare event simulation problem. In this approach, the importance sampling is done in two distinct phases. In the first phase, an importance sampling change of measure is used to bring the queue length up to the threshold at which low priority packets get rejected. In the second phase, a different importance sampling change of measure is used to move the queue length from the threshold to the buffer capacity.

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. This paper considers efficient simulation techniques for estimating steady-state quantities in models of highly dependable computing systems with general component failure and repair time distributions. Earlier approaches in this application setting for steady-state estimation rely on the regenerative method of simulation, which can be used when the failure time distributions are exponentially distributed. However, when the failure times are generally distributed the regenerative structure is lost and a new approach must be taken. The approach we take is to exploit a ratio representation for steady-state quantities in terms of cycles that are no longer independent and identically distributed. A "splitting" technique is used in which importance sampling is used to speed up the simulation of rare system failure events during a cycle, and standard simulation is used to estimate the expected cycle length. Experimental results show that the method is effective in practice. Keywords. Relia...

this paper, we review some of the importance-sampling techniques that have been developed in recent years to e#ciently estimate dependability measures in Markovian and non-Markovian models of highly dependable systems. 1 Acronyms MTTF Mean time to failure. MTBF Mean time between failures. CTMC Continuous-time Markov chain. DTMC Discrete-time Markov chain. GSMP Generalized semi-Markov process. SAVE System AVailability Estimator. CLT Central limit theorem. VRR Variance reduction ratio. TRR Total e#ort reduction ratio. MSDIS Measure-specific dynamic importance sampling. BLBLR Balance over links balanced likelihood ratio. BLBLRC Balance over links balanced likelihood ratio with cuts. 1 INTRODUCTION High dependability requirements of today's critical and/or commercial systems often lead to complicated and costly designs. The ability to predict relevant dependability measures for such complex systems is essential, not only to guarantee hig