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Insurance Mathematics And Economics Pdf

Insurance: Mathematics and Economics

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  • CiteScore: 1.58 ℹ CiteScore measures the average citations received per document published in this title. CiteScore values are based on citation counts in a given year (e.g. 2015) to documents published in three previous calendar years (e.g. 2012 – 14), divided by the number of documents in these three previous years (e.g. 2012 – 14).
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  • Impact Factor: 1.265Impact Factor:
    2017: 1.265
    The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years.
    2017 Journal Citation Reports (Clarivate Analytics, 2018)
  • 5-Year Impact Factor: 1.732Five-Year Impact Factor:
    2017: 1.732
    To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years.
    2017 Journal Citation Reports (Clarivate Analytics, 2018)
  • Source Normalized Impact per Paper (SNIP): 1.284Source Normalized Impact per Paper (SNIP):
    2017: 1.284
    SNIP measures contextual citation impact by weighting citations based on the total number of citations in a subject field.
  • SCImago Journal Rank (SJR): 1.083SCImago Journal Rank (SJR):
    2017: 1.083
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Insurance: Mathematics and Economics publishes leading research spanning all fields of actuarial science research. It appears six times per year and is the largest journal in actuarial science research around the world.

Insurance: Mathematics and Economics is an international academic journal that aims.

Insurance: Mathematics and Economics publishes leading research spanning all fields of actuarial science research. It appears six times per year and is the largest journal in actuarial science research around the world.

Insurance: Mathematics and Economics is an international academic journal that aims to strengthen the communication between individuals and groups who develop and apply research results in actuarial science. The journal feels a particular obligation to facilitate closer cooperation between those who conduct research in insurance mathematics and quantitative insurance economics, and practicing actuaries who are interested in the implementation of the results. To this purpose, Insurance: Mathematics and Economics publishes high-quality articles of broad international interest, concerned with either the theory of insurance mathematics and quantitative insurance economics or the inventive application of it, including empirical or experimental results. Articles that combine several of these aspects are particularly considered.

The subject matter of the journal includes the theory, models and methods of life insurance (including pension systems, social insurance, and health insurance), of non-life insurance, and of reinsurance and other risk-sharing arrangements. It also includes innovative insurance applications of results from related fields, such as probability and statistics, computer science and numerical analysis, quantitative economics, mathematical finance, operations research and management science, and, in particular, quantitative risk management.

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Insurance Risk and Ruin

This (lowercase (translateProductType product.productType)) has been cited by the following publications. This list is generated based on data provided by CrossRef.

David C. M. Dickson , University of Melbourne

  • Publisher: Cambridge University Press
  • Online publication date: January 2010
  • Print publication year: 2005
  • Online ISBN: 9780511624155
  • https://doi.org/10.1017/CBO9780511624155
  • Subjects: Economics, General Statistics and Probability, Statistics for Econometrics, Finance and Insurance, Finance and Accountancy, Statistics and Probability
  • Series: International Series on Actuarial Science

Email your librarian or administrator to recommend adding this book to your organisation’s collection.

  • Online ISBN: 9780511624155
  • Book DOI: https://doi.org/10.1017/CBO9780511624155

Book description

Based on the author’s experience of teaching final-year actuarial students in Britain and Australia, and suitable for a first course in insurance risk theory, this book focuses on the two major areas of risk theory – aggregate claims distributions and ruin theory. For aggregate claims distributions, detailed descriptions are given of recursive techniques that can be used in the individual and collective risk models. For the collective model, different classes of counting distribution are discussed, and recursion schemes for probability functions and moments presented. For the individual model, the three most commonly applied techniques are discussed and illustrated. Care has been taken to make the book accessible to readers who have a solid understanding of the basic tools of probability theory. Numerous worked examples are included in the text and each chapter concludes with exercises, which have answers in the book and full solutions available for instructors from www.cambridge.org/9780521846400.

‘… requires some mathematical maturity but provides a good insight into how probability distributions tie in with insurance applications.’

Source: Journal of Applied Statistics

‘… a nice introduction to some basic aspects of risk theory, with special emphasis on utility theory, recursive methods and ruin theory … What I appreciate most is the way in which the author explains the different topics dealt with in this book.’

Source: Publication of the International Statistical Institute

‘This book is well written. It is also well organized. … For practitioners, it may be of interesting reference, and a way to have a good overview of some recent developments in ruin theory.’

Source: ASTIN Bulletin

‘… a carefully and well written monograph on insurance risk and ruin, providing the higher-year student with the basic tools and concepts in these areas. Lecturers will find it a useful textbook for a corresponding course to teach in an actuarial program.’

Source: Zentralblatt MATH

‘All in all, this is a nice textbook, especially for students with a limited background in probability. In particular, it should be useful for students studying for the professional examination … I am not aware of any book on the same level in which ruin theory is treated so deeply.’

Source: Journal of the American Statistical Association

‘… provides an accessible treatment of some of the most fundamental concepts in the classical development of insurance portfolio modelling, admirably treading the tightrope between rigorous detail and intuitive argument … an excellent undergraduate treatment of an important and often daunting subject and will make a more than useful addition to the shelves of both actuarial educators and students alike.’

Source: Gazette of the Australian Maths Society

‘… this is a book which can well be recommended to students interested in risk and ruin and wanting a good readable account that goes beyond the syllabus of the professional examinations.’

Source: South African Actuarial Journal

‘… a good accessible treatment of some of the most fundamental concepts cleverly walking the fine line between too much rigorous detail and not enough. It is a good book for student reference in university libraries.’

Source: Mathematics Today

‘A clear, concise and well written textbook on two daunting actuarial areas … The exposition is so clear that it feels like [the author is] talking to you … This is an excellent book equally suitable for self-study and classroom instruction. It is highly recommended as supplementary reading for students studying for their professional exams and as an overview of the latest developments in risk models, ruin theory and reinsurance for practitioners.’

Seow Fan Chong Source: Annals of Actuarial Science

‘this well written and well organised book provides a good insight into how probability theory ties with insurance applications.’

Use of Mathematics in Economics

There have been rumors that mathematics is used in economics either for the deliberate purpose of mystification or to confer dignity upon common places as French was once used in diplomatic communications.

— James Newman (1907-1966, an American mathematician and mathematical historian)

What Is This All About?

When one studies economics for the first time, you will probably never come across any equations or calculations other than simple mathematics. There is much to read around basic concepts and understanding the various aspects of market, economy, business and understanding simple definitions of price, supply, demand, costs etc.

But as you delve further into this subject you realize there is more to it than just theory and talk. Besides what better way of explaining the concepts of prices, quantity of goods sold and costs without referring to numerical examples?

As students wanting to further their education in Economics, it rather helps to know your math.

An Example

One of the most basic concepts in Economics is the study of Demand & Supply. Why do suppliers sell at the price they do and what makes buyers buy at a particular price?

The theory will explain what is Demand? What is Supply?

Individual Demand is defined as the quantity that consumers are willing to buy a particular good at various prices.

Similarly, Supply is defined as the willingness of the supplier to provide the quantity of a particular good at various prices.

Now quantity and prices are denoted by numbers hence to define the above with numbers will be depicted as shown in the tables below. These are called the Demand and Supply Schedules.

Demand Schedule

Supply Schedule

Demand & Supply Curves

What table 1 shows about demand is that as the price of a particular good increases the quantity demanded falls. Now we observe this in our every day behaviour, don’t we? (exception is necessary goods and luxury items, but let us not get into that to avoid confusion to the reader). So basically there exists and inverse relation between price and quantity demanded for a particular good. Thus when one plots this on a graph wherein x- axis (horizontal line) depicts quantity and y-axis (vertical line) depicts price, the line formed by connecting the various points of price and matching quantities demanded will depict a downward sloping line or curve called the Individual Demand curve for a particular good.

In the same manner, as the price of particular good increases, suppliers are willing to supply more of that good. Naturally, since the more they sell at the higher price, the more money they make (in simple terms!). Hence there exists a positive relation between the price and quantity supplied of a particular good. When we plot these points on a graph and connect the points, the line is an upward sloping line or curve and is called the Individual Supply curve for a particular good.

The point at which the demand and supply curve intercepts is called the Point of Equilibrium – it is that level of price at which the quantity demanded and supplied is the same. Looking at the tables, you will observe, it is at the price of $4 that a quantity of 8 is supplied and demanded and hence is the equilibrium price and quantity for the particular good.

The Number Game

As you can see, we are using numbers, graphs and next we will be using equations to solve for either of the variables and hence mathematics is starting to mingle with the economic concepts and helps us actually understand better what the theory states. So you need your fundamentals in algebra, geometry, calculus all brushed up for starters and then linear programming and matrices, vectors and sets for others!

The simple linear equation (since it is a straight line) for the demand curve is q=a-bp where q is quantity, p is price and a and b are constants. The relation between quantity demanded at various prices being an inverse one implies the line has a negative slope. We can also depict this in relation to price.

As you move to further related topics to say market demand curves (summation of individual demand curves) or change in demand or calculating the elasticity of demand, each concept is corroborated with mathematical examples. One definitely needs clarity on solving for those to grasp these fundamental economic concepts.

Probably if you are fairly confident about your knowledge in Statistics and Statistical Tools , that too will help a lot in studying as well as applying Economics. Whether it is Micro economics, Production Systems, Economics growth, Macro economics, it is hard to explain as well as understand the theory without the use of mathematics. Although Adam Smith’s (considered the Father of Economics) famous work – ‘The Wealth of Nations’ published in 1776 has almost no mathematics in it. But it was noted that in the 19 th century Mathematics was considered a means to reaching the truth; logic and rationale made it imperative to use mathematics to prove any theorems. Many problems posed in economics hence motivated and were actually solved by mathematics.

Mathematicians & Economists

Analysis and study in economics help explain the interdependent relation between different variables. They try to explain what causes rise in prices or unemployment or inflation. Mathematical functions are modes through which these real life phenomena are made more understandable and logical.

Indeed there has been long standing argument on how important is mathematical works relevant for economics and the uses of economics. It is interesting to know that a number of economists have been awarded the Nobel Prize for their application of mathematics to economics including the first one awarded in 1969 to Ragnar Frisch and JanTinbergen. Leonid Kantorovich won a Nobel prize in 1975 in economics and he was a mathematician!

Many students who are looking to pursue a career in economics are advised to take a course in Mathematics since graduate level studies involve a lot more complex mathematics which is important to carry out research.

Stable and Unstable Equilibrium

by Sundaram Ponnusamy 9

Economics For Beginners: Supply And Demand

by Shawn McIntyre 6

The Hicksian Method and The Slutskian Method

by Sundaram Ponnusamy 21

Equilibrium Price Determination in the Market Period and Short Period Under Perfect Competition

by Sundaram Ponnusamy 2

Raymond Agabi

Great job. Your explanation being relevant, is well explicated.

amoo isaac

any disadvantages using mathematics in teaching economics

Vikky Nainiwal

Economics is a subject I love. This is a fantastic description of supply and demand. I will definitely look forward to reading more of your work.

Cletus A Inji

Thanks for nourishing the wonderful family of Economists. Upcoming generations should note.

Venkatachari M

3 years ago from Hyderabad, India

Very interesting topic on the use of mathematics in economics. You have described it well with some good examples. Voted up.

stanfrommarietta

As a quantitative psychologist with recent interests in heterodox economics like MMT, I view with suspicion the elevation of mathematics without a corresponding check of whether the mathematical model accurately represents reality. I think the received view in economics today known as neo-classical economics, seeks to build its theories on behavior of an individual and homogeneous sets of individuals. Because individuals often vary considerably in their behavior in psychology, I am suspicious of the arm-chair reasoning based on ideal, rational individuals. And I am suspicious about the applicability of certain forms of mathematics to represent behavior of heterogenous groups of individuals each reacting differently to various goods and services. I doubt the validity of the equilibrium theory of markets. And I doubt that linear equations are sufficient to describe aggregates of heterogeneous groups and goods and services. Steve Keen has a book “Debunking Economics”, written in a beautifully clear and entertaining form that debunks, assumption by assumption the foundational assumptions of neo-classical economics. He notes how limited most neo-classical economists are in their mathematical preparation. Few have any mastery of differential equations. But Keen is developing complex flow models of aggregates of money that does not assume equilibrium and effectively builds on non-linear differential equations with feedbacks and loops. He predicted on the basis of his model of the economy that included private debt of the housing market, that there would be a collapse of the economy after a period of seeming stability. And he predicted this before the crash of 2007-2008. No neo-classical economists saw it coming. Private debt was not something they considered.

Mathematics is only useful to the extent that models within it accurately mirror reality. Beautiful and complex mathematics can be meaningless when it doesn’t correspond to reality. And it is always possible to fit any complex mathematical model to a given set of date if you estimate enough parameters of the model, equal in number to the data points. Mathematical models need to be tested against the real world. And testing must build in enough fixed/specified parameters not estimated to make it possibile for the model not to fit if reality differs from the model.

umbrarchist

Yeah, do the math. Compute and report Demand Side Depreciation. Don’t cars purchased by consumers wear out? How about $300,000,000,000 per year for just the United States. That is an estimate based on 1995 data when there were 200,000,000 cars.

JP Carlos

6 years ago from Quezon CIty, Phlippines

I understand the importance of mathematics in economics or in everyday life. The problem is tht it does not understand me back. lol

In high school we had several mathematics classes including on in business math and economics. It was a nightmare for me back then. Little do i know, I’,, be using the info now that I’m working.

Riverfish24

6 years ago from United States

Thanks a lot Simone! I wish, my prof had been as patient and easier on us too!

Simone Haruko Smith

6 years ago from San Francisco

What a fabulous explanation! I wish my first economics professor had explained this so well. Love the helpful examples, tables, and graphic. You rock!!

Riverfish24

6 years ago from United States

Yay! Thanks meloncauli, that was the idea!

meloncauli

6 years ago from UK

Interesting hub and very well written. I thought this would go over the top of my head when I read the title ( as lindacee) but you did make it easy to understand. I learned something today!

Riverfish24

6 years ago from United States

tirelesstraveler – thank you for the stop by amidst all your travels! 🙂

Judy Specht

6 years ago from California

Splendid explanation of supply and demand. Voted up, interesting and useful.

Riverfish24

6 years ago from United States

Thank you wrenfrost56, I am glad you found it an easy read.

wrenfrost56

6 years ago from U.K.

Well written, well presented and easy to understand, you have done a great job with this hub. 🙂

Riverfish24

6 years ago from United States

Thanks Krsharp05 Om & Lindacee – that was the very idea, to explain it in simple terms !

Chemistry Book & Leahlefler- yes, very true!

Robert & cassyLu – thanks for the confidence and votes!

lindacee

6 years ago from Arizona

The title made me a bit tentative to dive in. I was a dismal failure in math (did not take statistics and no economics courses either) and thought it would be way over my head. I was pleasantly surprised to find it to be a good read and easy to comprehend. Well done. I just hope there’s no test! 😉

Chemistry Book

There was a time when the impression was that mathematics in economics terminates in statistics. But it became clear there are array of instances where calculus is used to explain economic principles.

Om Paramapoonya

As someone who’s awfully bad at math, I have to admit I was somewhat discouraged to read this hub when I first saw the title! LOL. I’m glad I read it, though. Very well-written, interesting and much easier to follow than I thought it would be. Rated up!

CassyLu1981

6 years ago from Spring Lake, NC

Incredible hub 🙂 very informative and well written! Voted up and shared 🙂

Robert Erich

6 years ago from California

Economics is a subject I love. This is a fantastic description of supply and demand. I will definitely look forward to reading more of your work.

Kristi Sharp

6 years ago from Born in Missouri. Raised in Minnesota.

You’ve done an excellent job breaking down and explaining demand and supply into terms that are easy to understand. Interesting and useful.

Leah Lefler

6 years ago from Western New York

Economics – the dismal science! I love your explanation of how mathematics is an integral part of economics now, when it wasn’t really included in 19th century writings. Mathematics plays the primary role in many sciences (physics, chemistry, etc.) and it is really the backbone of modern economics.

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