This document discusses methods for calculating and comparing investment returns and wealth over time. It defines formulas for calculating periodic returns, cumulative returns, expected returns, variance of returns, and wealth as an exponential function of cumulative returns. It also discusses how to calculate ratios comparing the terminal wealth of different investments and percentile distributions of terminal wealth.
Whenever we want to perform analysis of an algorithm, we need to calculate the complexity of that algorithm. But when we calculate complexity of an algorithm it does not provide exact amount of resource required. So instead of taking exact amount of resource we represent that complexity in a general form (Notation) which produces the basic nature of that algorithm. We use that general form (Notation) for the analysis process.
The little Oh (o) notation is a method of expressing the an upper bound on the growth rate of an algorithm’s
running time which may or may not be asymptotically tight therefore little oh(o) is also called a loose upper
bound we use little oh (o) notations to denote upper bound that is asymptotically not tight.
Whenever we want to perform analysis of an algorithm, we need to calculate the complexity of that algorithm. But when we calculate complexity of an algorithm it does not provide exact amount of resource required. So instead of taking exact amount of resource we represent that complexity in a general form (Notation) which produces the basic nature of that algorithm. We use that general form (Notation) for the analysis process.
The little Oh (o) notation is a method of expressing the an upper bound on the growth rate of an algorithm’s
running time which may or may not be asymptotically tight therefore little oh(o) is also called a loose upper
bound we use little oh (o) notations to denote upper bound that is asymptotically not tight.
The Big Omega () notation is a method of expressing the lower bound on the growth rate of an algorithm’s
running time. In other words we can say that it is the minimum amount of time, an algorithm could possibly
take to finish it therefore the “big-Omega” or -Notation is used for best-case analysis of the algorithm.
The Theta (Θ) notation is a method of expressing the asymptotic tight bound on the growth rate of an
algorithm’s running time both from above and below ends i.e. upper bound and lower bound.
The Big Omega () notation is a method of expressing the lower bound on the growth rate of an algorithm’s
running time. In other words we can say that it is the minimum amount of time, an algorithm could possibly
take to finish it therefore the “big-Omega” or -Notation is used for best-case analysis of the algorithm.
The Theta (Θ) notation is a method of expressing the asymptotic tight bound on the growth rate of an
algorithm’s running time both from above and below ends i.e. upper bound and lower bound.
Research Inventy : International Journal of Engineering and Scienceresearchinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
These slides provide a preliminary risk pricing presentation in Farsi. We have used risk models of Nobel Laureates to explain some basic risk concepts. This package is one of the series of slides focusing on risk management. There will be more slides on the topic shared through SlideShare.
Common and private ownership of exhaustible resources: theoretical implicat...alexandersurkov
K. Bosrissov, A. Surkov. Common and private ownership
of exhaustible resources:
theoretical implications for
economic growth. Presented at PET10 – 11th Annual Conference of the Association for
Public Economic Theory, Istanbul, Turkey, June 25-27, 2010
Nonlinear Stochastic Programming by the Monte-Carlo methodSSA KPI
AACIMP 2010 Summer School lecture by Leonidas Sakalauskas. "Applied Mathematics" stream. "Stochastic Programming and Applications" course. Part 4.
More info at http://summerschool.ssa.org.ua
WAVELET-PACKET-BASED ADAPTIVE ALGORITHM FOR SPARSE IMPULSE RESPONSE IDENTIFI...bermudez_jcm
Presented at IEEE ICASSP-2007:
This paper proposes a wavelet-packet-based (WPB) algorithm for efficient identification of sparse impulse responses with arbitrary frequency spectra. The discrete wavelet packet transform (DWPT) is adaptively tailored to the energy distribution of the unknown system\'s response spectrum. The new algorithm leads to a reduced number of active coefficients and to a reduced computational complexity, when compared to competing wavelet-based algorithms. Simulation results illustrate the applicability of the proposed algorithm.
4. Z Score * * N
Percentilefor r(t )
6 e5 e 0.68242 e1.00 e1.31758
Ter min alWealthofManagerN
RatioofCumulativeWealthN
Ter min alWealthofBenchmark N
r( t )
Ter min alWealthofManagerN X *e X * (1 R1 ) * (1 R2 ) * ... * (1 R N )
r( t )
Ter min alWealthofBenchmark N X *e X * (1 R1 ) * (1 R2 ) * ... * (1 R N )
6. Rt rt
1 Rt (k )
1 Rt (k ) (1 Rt ) * (1 Rt 1 ) * (1 Rt 2 )....(1 Rt k 1 )
e rt ( k ) e ( rt ) * e ( rt 1 ) * ... * e ( tt k 1 )
r
e rt ( k ) e ( t )
rt (k ) k
rt (k ) ln[1 Rt (k )]
rt (k ) ln[(1 Rt ) * (1 Rt 1 )....(1 Rt k 1 )]
rt (k ) rt rt 1 ... rt k 1
UnitValue N (1 R1 ) * (1 R2 ) * ... * (1 R N )
r( t )
UnitValue N e
7. r( t )
Ter min alWealthN X *e X * (1 R1 ) * (1 R2 ) * ... * (1 R N )
r(t )
rt
r(t )
~N( ,
~N( , ~N( + , +
e( )
e( *t )
e( )
e( )
( )
e
2* * 2
* t
r(t )
E N ( r(t ) ) *N
r(t )
2 2
N ( rt ) *N
r(t )
N ( rt ) * N
r(t )
PercentileDistributionofTer min alWealthN e(Z Score* * N )
8. Sumofall Re turns r( t )
Numberof Re turns N
(r( t ) r )2
N 1
r( t )
Ter min alWealthofManagerN X *e X * (1 R1 ) * (1 R2 ) * ... * (1 R N )
RN
r( t )
Ter min alWealthofBenchmark N X *e X * (1 R1 ) * (1 R2 ) * ... * (1 R N )
RN
Ter min alWealthofManagerN
RatioofCumulativeWealthN
Ter min alWealthofBenchmark N