A generalization of Hull and White formula and applications to option pricing approximation

By means of Malliavin Calculus we see that the classical Hull and White formulafor option pricing can be extended to the case where the noise driving thevolatility process is correlated with the noise driving the stock prices. Thisextension will allow us to construct option pricing approximation formulas.Numerical examples are presented.

On the efficiency and sensitivity of a pyramidal classification algorithm

In this paper we propose a Pyramidal Classification Algorithm,which together with an appropriate aggregation index producesan indexed pseudo-hierarchy (in the strict sense) withoutinversions nor crossings. The computer implementation of thealgorithm makes it possible to carry out some simulation testsby Monte Carlo methods in order to study the efficiency andsensitivity of the pyramidal methods of the Maximum, Minimumand UPGMA. The results shown in this paper may help to choosebetween the three classification methods proposed, in order toobtain the classification that best fits the original structureof the population, provided we have an a priori informationconcerning this structure.

A decomposition formula for option prices in the Heston model and applications to option pricing approximation

By means of classical Itô's calculus we decompose option prices asthe sum of the classical Black-Scholes formula with volatility parameterequal to the root-mean-square future average volatility plus a term dueby correlation and a term due to the volatility of the volatility. Thisdecomposition allows us to develop first and second-order approximationformulas for option prices and implied volatilities in the Heston volatilityframework, as well as to study their accuracy. Numerical examples aregiven.

A simple randomized algorithm for consistent sequential prediction of ergodic time series

We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from recent developments of the theory of the prediction of individual sequences. We show that if thesequence is a realization of a stationary and ergodic random process then the average number of mistakes converges, almost surely, to that of the optimum, given by the Bayes predictor.

MSISpIC: A Probabilistic Scan Matching Algorithm Using a Mechanical Scanned Imaging Sonar

This paper compares two well known scan matching algorithms: the MbICP and the pIC. As a result of the study, it is proposed the MSISpIC, a probabilistic scan matching algorithm for the localization of an Autonomous Underwater Vehicle (AUV). The technique uses range scans gathered with a Mechanical Scanning Imaging Sonar (MSIS), and the robot displacement estimated through dead-reckoning with the help of a Doppler Velocity Log (DVL) and a Motion Reference Unit (MRU). The proposed method is an extension of the pIC algorithm. Its major contribution consists in: 1) using an EKF to estimate the local path traveled by the robot while grabbing the scan as well as its uncertainty and 2) proposing a method to group into a unique scan, with a convenient uncertainty model, all the data grabbed along the path described by the robot. The algorithm has been tested on an AUV guided along a 600m path within a marina environment with satisfactory results

An Efficient Nominal Unification Algorithm

Nominal Unification is an extension of first-order unification where terms can contain binders and unification is performed modulo α equivalence. Here we prove that the existence of nominal unifiers can be decided in quadratic time. First, we linearly-reduce nominal unification problems to a sequence of freshness and equalities between atoms, modulo a permutation, using ideas as Paterson and Wegman for first-order unification. Second, we prove that solvability of these reduced problems may be checked in quadràtic time. Finally, we point out how using ideas of Brown and Tarjan for unbalanced merging, we could solve these reduced problems more efficiently

Incremental neural networks for function approximation

A new strategy for incremental building of multilayer feedforward neural networks is proposed in the context of approximation of functions from R-p to R-q using noisy data. A stopping criterion based on the properties of the noise is also proposed. Experimental results for both artificial and real data are performed and two alternatives of the proposed construction strategy are compared.

Validation of a clinical algorithm to identify low-risk patients with pulmonary embolism.

Summary Background: We previously derived a clinical prognostic algorithm to identify patients with pulmonary embolism (PE) who are at low-risk of short-term mortality who could be safely discharged early or treated entirely in an outpatient setting. Objectives: To externally validate the clinical prognostic algorithm in an independent patient sample. Methods: We validated the algorithm in 983 consecutive patients prospectively diagnosed with PE at an emergency department of a university hospital. Patients with none of the algorithm's 10 prognostic variables (age >/= 70 years, cancer, heart failure, chronic lung disease, chronic renal disease, cerebrovascular disease, pulse >/= 110/min., systolic blood pressure < 100 mm Hg, oxygen saturation < 90%, and altered mental status) at baseline were defined as low-risk. We compared 30-day overall mortality among low-risk patients based on the algorithm between the validation and the original derivation sample. We also assessed the rate of PE-related and bleeding-related mortality among low-risk patients. Results: Overall, the algorithm classified 16.3% of patients with PE as low-risk. Mortality at 30 days was 1.9% among low-risk patients and did not differ between the validation and the original derivation sample. Among low-risk patients, only 0.6% died from definite or possible PE, and 0% died from bleeding. Conclusions: This study validates an easy-to-use, clinical prognostic algorithm for PE that accurately identifies patients with PE who are at low-risk of short-term mortality. Low-risk patients based on our algorithm are potential candidates for less costly outpatient treatment.

A fast Bayesian reconstruction algorithm for emission tomography with entropy prior converging to feasible images

The development and tests of an iterative reconstruction algorithm for emission tomography based on Bayesian statistical concepts are described. The algorithm uses the entropy of the generated image as a prior distribution, can be accelerated by the choice of an exponent, and converges uniformly to feasible images by the choice of one adjustable parameter. A feasible image has been defined as one that is consistent with the initial data (i.e. it is an image that, if truly a source of radiation in a patient, could have generated the initial data by the Poisson process that governs radioactive disintegration). The fundamental ideas of Bayesian reconstruction are discussed, along with the use of an entropy prior with an adjustable contrast parameter, the use of likelihood with data increment parameters as conditional probability, and the development of the new fast maximum a posteriori with entropy (FMAPE) Algorithm by the successive substitution method. It is shown that in the maximum likelihood estimator (MLE) and FMAPE algorithms, the only correct choice of initial image for the iterative procedure in the absence of a priori knowledge about the image configuration is a uniform field.

A fully adaptive numerical approximation for a two-dimensional epidemic model with nonlinear cross-diffusion

An epidemic model is formulated by a reactionâeuro"diffusion system where the spatial pattern formation is driven by cross-diffusion. The reaction terms describe the local dynamics of susceptible and infected species, whereas the diffusion terms account for the spatial distribution dynamics. For both self-diffusion and cross-diffusion, nonlinear constitutive assumptions are suggested. To simulate the pattern formation two finite volume formulations are proposed, which employ a conservative and a non-conservative discretization, respectively. An efficient simulation is obtained by a fully adaptive multiresolution strategy. Numerical examples illustrate the impact of the cross-diffusion on the pattern formation.

Ruin Theory with Excess of Loss Reinsurance and Reinstatements

The present paper studies the probability of ruin of an insurer, if excess of loss reinsurance with reinstatements is applied. In the setting of the classical Cramer-Lundberg risk model, piecewise deterministic Markov processes are used to describe the free surplus process in this more general situation. It is shown that the finite-time ruin probability is both the solution of a partial integro-differential equation and the fixed point of a contractive integral operator. We exploit the latter representation to develop and implement a recursive algorithm for numerical approximation of the ruin probability that involves high-dimensional integration. Furthermore we study the behavior of the finite-time ruin probability under various levels of initial surplus and security loadings and compare the efficiency of the numerical algorithm with the computational alternative of stochastic simulation of the risk process. (C) 2011 Elsevier Inc. All rights reserved.