Peter Pflaumer

TU Dortmund University | TUD · Faculty of Statistics

Since the mortality of modern developed population is largely the mortality of old age, the Gompertz model provides a good approximation of life tables in these populations and can be used to estimate and forecast many parameters of the life table and the corresponding stationary population. Average and median remaining life expectancies are calcul...

This study examines the relationship between gold prices and global GDP using ARIMAX models, comparing two primary approaches: the log-level ARIMAX(1,0,1) model and the first-difference logarithmic model. The analysis spans the period from 1970 to 2023 and highlights the gold price's sensitivity to global economic dynamics. The log-level model demo...

This paper presents a stochastic approach to partial firm valuation by analyzing casino hold percentages using Random Walk and ARMA(1,1) models. We establish a mathematical framework that models future cash flows as influenced by current values and random disturbances, enabling us to derive variance formulas for discounted cash flows. By treating c...

Predicting trends in Sex Ratio at Birth (SRB) is crucial in demographic research, shedding light on evolving population dynamics. This study conducts a thorough investigation into the selection and evaluation of optimal forecasting models for SRB data. Utilizing historical SRB records from selected countries, we meticulously assess various models,...

This study offers a comprehensive exploration of gold price forecasting, with a particular emphasis on the intricate drift component within ARIMA models. It introduces sensitivity analysis as a strategic approach to address the complexities inherent in forecasting gold prices and provides practical recommendations tailored for investors. By integra...

This article presents a method for estimating the variance of the firm or enterprise value distribution by incorporating temporal dependencies in cash flows using ARMA models. The analysis highlights the importance of considering these dependencies, as neglecting them can lead to a significant increase in variance and subsequent erroneous decision-...

Excel Formulas for Financial Mathematics and Investment Analysis provides a practical approach to applying financial principles using Excel. Unveiling the power of Excel, this comprehensive guide explores topics from compound interest to bond pricing. Featuring key functions like NPV, RATE, IRR, and more, it seamlessly blends practical Excel applic...

Age-specific mortality rates for semi-supercentenarians and supercentenarians play a pivotal role in comprehending longevity and population dynamics at advanced ages. In this study, we introduce a modified Wittstein Model, offering an alternative to the conventional S-shaped curve models used in mortality forecasting. The Wittstein Model, originall...

The old-age dependency ratios are indicators of the number of elderly people who are generally economically inactive compared to the number of people of working age. They significantly affect the financial burden of social public pension schemes, making it essential to analyze the influence of mortality on this ratio. In this paper, the Gompertz mo...

Thomas Young (1773-1829) is one of the greatest thinkers and polymaths. His scientific work includes significant contributions in the fields of medicine, physics , anthropology and ancient history. Less well known, however, is Young's demographic contribution. In 1826, Thomas Young examined graphical curves of mortality of his epoch (decrement tabl...

In 1761, the German demographer Johann Peter Süßmilch published a simple population growth model that starts with a couple, in the eighth chapter of his book “Die göttliche Ordnung” (The Divine Order). With the help of the Swiss mathematician Leonhard Euler, the population has been projected for 300 years. Euler and Süßmilch demonstrate that after...

Das vorliegende Übungsbuch ist die ideale Ergänzung zu: Ihrig, H.; Pflaumer, P: Finanzmathematik – Intensivkurs. Es enthält eine Zusammenstellung von 75 Klausuraufgaben der Finanzmathematik, die in den letzten Jahren im Fach Wirtschaftsmathematik gestellt worden sind. Mit zahlreichen Übungs- bzw. Klausuraufgaben findet man das Wichtigste zu jedem G...

Dieses Buch enthält eine Zusammenstellung von Klausuraufgaben in deskriptiver Statistik. Daher dient es in erster Linie einer schnellen und effizienten Prüfungsvorbereitung. Es ist die ideale Ergänzung zu dem bereits erschienenen Lehrbuch Pflaumer, P; Heine, B; Hartung, J: Statistik für Wirtschafts- und Sozialwissenschaften: Deskriptive Statistik....

In der vorliegenden Schrift werden wichtige finanzmathematische Formeln und Funktionen in Excel anhand vieler Beispiele der Finanzmathematik und der Investitionsrechnung übersichtsartig erläutert. Als theoretische Grundlage der Finanzmathematik und der Investitionsrechnung dienen die Lehrbücher von Ihrig, H; Pflaumer, P: Finanzmathematik – Intensiv...

The renowned Swiss mathematician Leonhard Euler created three variations of a simple population projection model, including one stable model and two non-stable models, that consider a couple with different fertility behaviors and lifespans. While one of the models was published by a German demographer, Johann Peter Süßmilch, in his book "The Divine...

Das Skript ist aus Vorlesungen der Bevölkerungsstatistik und Demographie an der Fakultät Statistik der TU Dortmund hervorgegangen. Methodischen Grundlagen mit zahlreichen Anwendungen werden dargestellt (Version vom 10.6.2021). Inhalt: Kap 1: Einführung (Begriffe, Theorien, Datengewinnung), Kap 2: Entwicklung der Gesamtbevölkerung (Historische Ent...

Average per capita energy consumption is forecast using modern time series models, the Autoregressive Integrated Moving Average (ARIMA) models. Finally, the results of the time series forecasts are combined with stochastic UN world population projections to obtain forecasts and prediction intervals of total energy consumption from 2022 to 2050. The...

Übungsaufgaben und Lösungshinweise der deskriptiven Statistik für unser Lehrbuch: Pflaumer; Heine; Hartung: Deskriptive Statistik, 4. Aufl., München 2009

Zusammenfassung Einleitung (Über)sterblichkeit und verlorene Lebensjahre sind wichtige Maße für gesundheitliche Risiken durch die Corona-Pandemie. Das Ziel dieses Beitrags ist es, methodische Faktoren zu benennen, die die Berechnung der Sterblichkeit beeinflussen, und auf mögliche Fehlinterpretationen von verlorenen Lebensjahren hinzuweisen. Method...

After presenting simulation results of different Labouchere betting systems and comparisons with martingale betting, the paper focuses in chapter 4 on the statistical profit distribution of a Labouchere round, which can be approximated by a mixed random variable with the Gompertz-Gumbel distribution as a smoothing function. The nearly continuous lo...

The predicted number of deaths is compared with the actual number of deaths to evaluate the predictive power of a seasonal ARIMA model.

Continuous models of population dynamics are used to estimate the intrinsic growth rate and other demographic characteristics of blue whale populations. The basis of my investigation is an article by Branch (2008), who estimated the mean annual growth rate as 4.1%, using a simple survival function.

In this statistical presentation, based on and continuing Pflaumer's research: A Graphical Analysis of Weekly Deaths in Germany during the Corona Pandemic, 2020 , weekly deaths in Germany during the first 52 calendar weeks of 2020 and 2021 are analyzed.

This study delves into blue whale population dynamics and demographic modeling, emphasizing the repercussions of historical industrial hunting and the subsequent population decline. Employing continuous demographic models, we calculate intrinsic growth rates, construct life tables, and formulate stable population models. The research underscores th...

The predicted number of deaths is compared with the actual number of deaths to evaluate the predictive power of a seasonal ARIMA model. Additionally, ratios for excess deaths are calculated. The data can be seen in the appendix.

Graphs and statistics of weekly deaths for selected age groups in Germany for 2020 and 2021 are presented. Excess mortality is calculated and it is shown that the result is just below 4 percent compared to 2020. If the demographic effects of age structure changes are taken into account, especially in the over-80 age group, total excess mortality is...

This article analyzes the stochastic aspects of a tontine using a Gompertz distribution. In particular, the probabilistic and demographic risks of a tontine investment are examined. The expected value and variance of tontine payouts are calculated. Both parameters increase with age. The stochastic present value of a tontine payout is compared with...

This article proposes a quick and easy to understand procedure for evaluating the risk in investment appraisal. The calculations can be performed using Excel. We develop a simple stochastic model for assessing the risk of a capital investment project. The distribution of the net present value (NPV) depends on stochastic and deterministic influence...

Excess deaths will be defined as the difference between the observed number of deaths in a specific period and the expected number of deaths in the same period. Excess death estimates can be calculated in several ways, and differ depending on the methodology used and the assumptions made about how many deaths are likely to occur. Often, a simple an...

Introduction Excess mortality is a suitable indicator of health consequences of COVID-19 because death from any cause is clearly defined contrary to death from Covid-19. We compared the overall mortality in 2020 with the overall mortality in 2016 to 2019 in Germany, Sweden and Spain. Contrary to other studies, we also took the demographic developme...

This article analyzes the stochastic aspects of a tontine using a Gompertz distribution. In particular, the probabilistic and demographic risks of a tontine investment are examined. The expected value and variance of tontine payouts are calculated. Both parameters increase with age. The stochastic present value of a tontine payout is compared with...

In dieser Projektarbeit ist es das Ziel, die Todesfälle des Jahres 2021 mit denen der vorherigen Jahre zu vergleichen. Damit soll ermittelt werden, ob die Corona-Pandemie die Todeszahlen Deutschlands beeinflusst hat

Diese Schrift ist aus Vorlesungen, Seminaren und Beratungsfällen hervorgegangen, die ich in den letzten Jahren durchgeführt habe. Ziel ist es, die wichtigsten Verfahren der Investitionsrechnung an einem kurzgefassten Lehrtext vorzustellen. Die Schrift dient der schnellen Vermittlung von Basiswissen. Ein Übungsteil mit Lösungshinweisen schließt den...

Updated Results: Excess deaths in 36 European countries and the United States are calculated by comparing the current deaths with the average across previous years. It turns out that these countries were affected very differently by excess mortality in 2020. Times series of weekly deaths for all countries between 2016 and 2020 are analyzed. Excess...

In this report, weekly deaths in Germany from 2016 to 2020 are analyzed. Data are obtained from the German Federal Statistical Office. The data set includes 260 observations and five variables: deaths of all persons, and deaths of persons in the age groups 0-40, 40-60, 60-80, and 80-100 years. Times series of weekly deaths and measures of excess mo...

The number of deaths in Germany in the first half of 2020 is about 477.5 thousand (preliminary results from January 1 to June 28), which is close to the average of the previous years 2016 to 2019.

This report (handout) for my classes in demography and life table analysis at the Technical University of Dortmund analyzes the daily death cases in Germany from 2016 until April 26, 2020. Data are provided by the Federal Statistical Office (Statistisches Bundesamt, Wiesbaden). Statistical computing and graphics have been made with R. The data set...

In 1761, the German demographer Johann Peter Süßmilch published a simple population growth model that starts with a couple, in the eighth chapter of his book Die göttliche Ordnung. With the help of the Swiss mathematician Leonhard Euler, he projected the population for 300 years. He demonstrated that after that time the population will be growing a...

Some gamblers use a martingale or doubling strategy as a way of improving their chances of winning. This paper derives important formulas for the martingale strategy, such as the distribution, the expected value, the standard deviation of the profit, the risk of a loss or the expected bet of one or multiple martingale rounds. A computer simulation...

In this paper, death probabilities derived from the Gompertz and Wittstein models are used to project mortality at advanced ages beginning at the age of 101 years. Life table data of Germany from 1871 to 2012 serve as a basis for the empirical analysis. Projections of the death probabilities and life table survivors will be shown. The increase of t...

Thousands of inscriptions of age at death from Roman epitaphs in North Africa are statistically analyzed. The Gompertz distribution is used to estimate survivor functions. The smoothed distributions are classified according to the estimation results. Similarities and differences can be detected more easily. Parameters such as mean, mode, skewness,...

Since uncertainty is the crucial point of a capital investment decision, risk analysis in capital budgeting is often applied. Usually risk analysis is carried out by a Monte Carlo simulation. The aim of this article is to present simple analytical methods which allow us to calculate the standard deviation of a project with correlated cash flows as...

Thousands of age at death inscriptions from Roman epitaphs are statistically analyzed. The Gompertz distribution is used to estimate survivor functions. The smoothed distributions are classified according to the estimation results. Similarities and differences can be detected more easily. Parameters such as mean, mode, skewness, and kurtosis are ca...

In this paper a life table for the Roman population is constructed using Ulpian’s table. This table can be regarded as a tool to compute the value of an annuity taking into account the age of the beneficiary. The Gompertz distribution and some of its extensions are applied for the life table construction. It is shown that the Roman life table can b...

August Zillmer (1831–1893) was a German life insurance actuary in Berlin. He is credited for one of the first German textbooks on actuarial mathematics. His name is associated with the Zillmer method of calculating life insurance reserves. In this paper, August Zillmer’s early contribution to demographic analysis, which is virtually unknown, is des...

Ulpian’s table is a famous ancient text that is preserved in edited form in Justinian’s Digest, a compendium of Roman law compiled by order of the emperor Justinian I in the sixth century AD. This passage probably provides a rough estimation of Roman life expectancy in the early third century AD. The paper begins with a discussion of the demographi...

A life table for the feral camel population in central Australia is constructed, using an extension of the Gompertz distribution, which was first proposed in a note by the famous mathematician Gauss. It is shown that under certain conditions some important life table parameters can be represented by simple formulae. The derived life table is then u...

Population forecasts have received a great deal of attention during the past few years. They are widely used for planning and policy purposes. In this paper, the Gompertz growth curve is proposed to forecast the U.S. population. In order to evaluate its forecast error, population estimates from 1890 to 2010 are compared with the corresponding predi...

The old-age dependency ratio is the ratio of the number of elderly people at an age when they are generally economically inactive, compared to the number of people of working age. It is an indicator of how many potential retirees a potential worker has to support. In the following paper the influence of mortality on the old-age-dependency ratio is...

Es wird zunächst ein Überblick über die gängigen Methoden der Sterblichkeitsmodellierung gegeben. Von besonderem Interesse sind Vorhersagen. Ein Schwerpunkt der Arbeit liegt in diesem Zusammenhang auf dem Brass-Verhältnismodell. In einer ex-post Studie an deutschen Daten führt dieser Ansatz zu ebenso guten Prognosen wie die normalerweise verwendete...

The rectangularization of life tables is defined as a trend towards a more rectangular shape of the survival curve due to increased survival and concentration of deaths around the mean age at death. Since the mortality of modern developed population is largely the mortality of old age, the Gompertz model provides a good approximation of life tables...

First, this paper investigates the properties of the Gompertz distribution and the relationships of their constants. Then the use of Gompertz´s law to describe mortality is discussed with male and female period life table data of the United States between 1900 and 2000. For this purpose a model incorporating time trends has been formulated with age...

Summary Forecasts for the number of students in Germany are conducted by the Kultusministerkonferenz. They use a transition model which does not allow for prediction intervals and therefore lack a measure of uncertainty of the forecast. Since the uncertainty is high for such forecasts, this lack is of importance. In this paper, structural ratios,...

Die stochastische Investitionsrechnung, ob sie nun simulativ oder analytisch durchgeführt wird, ist ein geeignetes Instrument zur Identifizierung und Bewertung von Risiken bei Investitionsentscheidungen. Dieser Beitrag soll die Grundzüge der stochastischen Investitionsrechnung darstellen und an einem einfachen Beispiel demonstrieren.

Methods from mathematics of finance and demography are presented in order to investigate the influence of migration on the long-term population development. Methods from mathematics of finance do not take the age structure of a population into consideration and can therefore only be used as an approximation. The less the age structures in question...

The mortality of German joint stock companies is investigated using life table techniques. An lDB-distribution or Hjorth-distribution and an exponential distribution are fitted to the hazard rates, whereby the population is divided into small and large firms. Survivor functions and life expectanry functions are presented. The life expectancy of all...

The accuracy of U.N. population projections is examined. The goal is to measure the amount of uncertainty associated with past projections of the United Nations in order to provide a realistic measure of the uncertainty in the projection that the U.N. ma,kes in the future. Various descriptive measures of the forecast error data set are presented au...

The objective of this paper is to examine the effect of migration on the size and the age structure of the population in Germany by applying population projection models.

"The use of the Box-Jenkins approach for forecasting the population of the United States up to the year 2080 is discussed. It is shown that the Box-Jenkins approach is equivalent to a simple trend model when making long-range predictions for the United States. An investigation of forecasting accuracy indicates that the Box-Jenkins method produces p...

In this paper the accuracy of population forecasts is discussed. Various papers on errors of population forecasting are reviewed and summarized. The results are stated in six theses. The main findings show that no clear dominance of any one forecasting method can be determined, that the logarithmic forecast errors are more or less independent of th...

The purpose of this paper is to test several empirical warrant pricing models.The influence of the valuation (under- and overvalued warrants) on future warrant prices is investigated.

The aim of this study is to empirically examine the suitability of various models for evaluating warrants. In particular, the influence of the under-and overvaluation on the future price development of the warrant is to be determined.

Using the age- and sex-specific data of 14 developed countries, we compare the short- to medium-term accuracy of ten principal component methods for forecasting mortality rates and life expectancy. These ten methods include the Lee-Carter method and many of its variants and extensions. For forecasting mortality rates, the weighted Hyndman-Ullah met...

"This paper presents an approach of constructing confidence intervals by means of Monte Carlo simulation. This technique attempts to incorporate the uncertainty involved in projecting the [West] German population by letting the fertility, mortality and net immigration rates vary as a random variable with a specific distribution. Since fertility and...

PIP: The aim of this paper is to describe several methods for quantifying the amount of uncertainty inherent in population forecasts used to assess the impact of demographic processes on social security systems. Each method is briefly outlined, and its advantages and disadvantages are discussed. The primary emphasis is on stochastic population mode...

For judging the quality of population forecasting methods, the root mean square error (RMSE) has proven to be a useful tool. A suitable variance component model is proposed for calculating the variance of the RMSE. The method is demonstrated by an example.

In modernen Darstellungen zur Investitionsrechnung hat der Gesichtspunkt der Entscheidung unter Unsicherheit immer mehr an Bedeutung gewonnen. Die diesen Aspekt bercksichtigende Risikoanalyse hat sich in der Praxis bereits vielfach durchgesetzt. In der Regel werden hierzu Simulationen durchgefhrt. Ziel dieser Arbeit ist es, ein einfaches, aber sehr...

Die exakte Methode zur Berechnung eines Konfidenzintervalls f~r eine unbekannte Wahrscheinlichkeit auf der Basis der Binomialverteilung ist in der Anwendung h~ufig zu umst~ndlich und zu rechenaufwendig. Daher greift man auf N~herungsverfahren zurHck, die auf der Normalapproximation beruhen. Dies ist sicherlich unproblematisch, solange der Stichprob...

The aim of the article is to quantify the causes of inflation in the Federal Republic of Germany from 1962 to 1975. Price models with exogenous and endogenous wage rates are determined and econometrically estimated. The results show that both demand and cost factors have determined price developments.

Proefskrif (D.Sc.)--Dortmund, Univ., 1977.