RISK THEORY - LECTURE NOTES 1. INTRODUCTION The primary subject of Risk Theory is the development and study of mathematical and statistical models to describe and predict the behaviour of insurance portfolios‚ which are simply financial instruments composed of a (possibly quite large) number of individual policies. For the purposes of this course‚ we will define a policy as a random (or stochastic) process generating a deterministic income in the form of periodic premiums‚ and incurring financial
Premium Normal distribution Probability theory Variance
continuous measurements or features in a biometric system‚ such as vocal-tract related spectral features in a speaker recognition system. GMM parameters are estimated from training data using the iterative Expectation-Maximization (EM) algorithm or Maximum A Posteriori (MAP) estimation from a well-trained prior model. Main Body Text Introduction A Gaussian mixture model is a weighted sum of M component Gaussian densities as given by the equation‚ M wi g(x|µi ‚ Σi )‚ p(x|λ) = (1) i=1
Premium Normal distribution Variance
θ‚ 3 1 P(X = 3) = (1 − θ). 3 P(X = 1) = where 0 ≤ θ ≤ 1 is a parameter. The following 10 independent observations were taken from such a distribution: (3‚ 0‚ 2‚ 1‚ 3‚ 2‚ 1‚ 0‚ 2‚ 1). (a) Find the method of moments estimate of θ. (b) What is the maximum likelihood estimate of θ? (a) In general‚ let X1 ‚ X2 ‚ . . . ‚ Xn be a random sample drawn from this distribution. Since 2 1 2 1 7 µ1 = E[X] = 0 · θ + 1 · θ + 2 · (1 − θ) + 3 · (1 − θ) = − 2θ. 3 3 3 3 3 we have θ= and the MME for θ is 7 1 − µ1
Premium Probability theory Random variable Variance
Luc Bauwens . Winfried Pohlmeier David Veredas (Eds.) High Frequency Financial Econometrics Recent Developments With 57 Figures and 64 Tables Physica-Verlag A Springer Company High Frequency Financial Econometrics Recent Developments Prof. Winfried Pohlmeier Department of Economics University of Konstanz 78457 Konstanz Germany winfried.pohlmeier@uni-konstanz.de Prof. Luc Bauwens CORE Voie du Roman Pays 1348 Louvain-la-Neuve Belgium bauwens@ucl.ac.be Prof. David
Premium Foreign exchange market
strapdown magnetometers. The proposed calibration method is written in the sensor frame‚ and compensates for the combined effect of all linear time-invariant distortions‚ namely soft iron‚ hard iron‚ sensor non-orthogonality‚ bias‚ among others. A Maximum Likelihood Estimator (MLE) is formulated to iteratively find the optimal calibration parameters that best fit to the onboard sensor readings‚ without requiring external attitude references. It is shown that the proposed calibration technique is equivalent
Premium
The Key Role of the Volatility for Financial Engineering Dr. Zbigniew Krysiak zbigniew.krysiak@poczta.onet.pl Associate Professor of Finance - Warsaw School of Economics Visiting Professor at Northeastern Illinois University‚ Chicago Financial Mathematics Mathematics Department at Northeastern Illinois University‚ Chicago Wednesday‚ October 3rd‚ 2012 1 Agenda • Approaches to Modeling Volatilities • Volatility Models in Capital Allocation - VaR • Application of GARCH to Modeling
Premium Standard deviation Variance Autoregressive moving average model
impact on the yield curve while real activity has a milder and more persistent effect. We have some possible explanations for these findings which includes our particular construction of the credit variable and the validity of our large parametric maximum likelihood estimation. I am greatly
Premium Bond Normal distribution Factor analysis
This PDF is a selection from an out-of-print volume from the National Bureau of Economic Research Volume Title: The Economics of Aging Volume Author/Editor: David A. Wise‚ editor Volume Publisher: University of Chicago Press Volume ISBN: 0-226-90295-1 Volume URL: http://www.nber.org/books/wise89-1 Conference Date: March 19-22‚ 1987 Publication Date: 1989 Chapter Title: A Dynamic Programming Model of Retirement Behavior Chapter Author: John P. Rust Chapter URL: http://www.nber.org/chapters/c11588
Premium Economics Retirement Social Security
Recommended Action The Administrative Maximum (ADX) facility in Florence‚ Colorado utilizes the separate and silent strategy‚ so that offenders would reflect on their crimes all day‚ which started a debate on if it is healthy for inmates to undergo and whether is it a secure way to control inmates at the facility. Furthermore‚ to address the issue previously stated‚ I would recommend that the ADX change their strategy to the Auburn System‚ but change the prohibitions on the face-to-face contact
Premium Prison Eastern State Penitentiary Penology
of 5 m/s. What is the spring constant (in N/m)? 5. A 34-g bullet traveling at 120m/s embeds itself in a wooden block on a smooth surface. The block then slides toward a spring and collides with it. The block compresses the spring (k=100 N/m) a maximum of 1.25 cm. Calculate the mass of the block of wood. 6. If a force of 300N is exerted upon a 60 kg mass for 3 seconds‚ how much impulse does the mass experience? 7. An 80-kg man and his car are suddenly accelerated from rest to a speed of 5
Free Force Classical mechanics Mass