Försäkringsmatematik 7,5 högskolepoäng Actuarial Mathematics

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1 Försäkringsmatematik 7,5 högskolepoäng Actuarial Mathematics Kurskod: MMA713 Utbildningsnivå: Avancerad nivå Ämne: Matematik/Tillämpa Utbildningsområde Naturvetenskap d matematik : Giltig fr.o.m. termin: ht10 Huvudområde: Matematik/Tillämpa d matematik med fördjupning A1N Fastställandedatum Förändringsdatum: : Syfte Actuarial mathematics constitutes the mathematical foundation of the insurance business. The stochastic nature of accidents and the length of people s lives make uncertainty an integral part of this business. The course Actuarial Mathematics provides students with essential knowledge and tools required to explore the consequences of uncertainty as well as to solve other mathematical and statistical problems arising in the insurance business. It provides basics in the mathematical techniques which can be used to model and value cash flows dependent on death, survival, or other uncertainties depending on risks. The concepts of risk theory and risk processes are introduced. Various forms of life insurance and their mechanisms are considered. Insurance models, reinsurance contracts, different types of distributions and simulation methods for both claim sizes and claim numbers will be analysed in the framework of non-life insurance. Lärandemål At the end of the course the student is expected to be able to - describe and calculate compound interests and financial annuities. - operate with distribution functions and densities of future lifetime, the probabilities of survival/death, and force of mortality, and describe the construction and use of life tables. - define standard life insurance and annuity contracts (including the contracts with variable benefits) and to calculate the mean and variance of the present value of benefit payments under each of the standard contracts. - define and calculate net level premiums and evaluate net premium reserves in respect of the standard contracts. - describe and analyse claim flows (number of claims, claim amounts, aggregate claims amount, operate with claim size distributions, describe large and catastrophic claims, estimate and approximate characteristics of aggregate claim distributions, and calculate premiums). - use Cramèr-Lundberg's and other approximations for ruin probabilities. - describe basic models of reinsurance. - describe methods of stochastic modeling of insurance and reinsurance business. Innehåll Compound interests. Financial annuities. Lifetime distributions. Survival function. Life tables. Whole-life and term insurance. Pure endowments. Endowments. Life annuities. Net premiums. Net premium reserves. Claim flow (number of claims, claim amounts, aggregate claims amount). Claim number and claim size distributions (Poisson, mixed Poisson, Pareto, etc.). Premiums. Collective risk model. Recursive and approximate calculation of aggregate

2 claims distributions. Ruin probability. Cramèr-Lundberg's and other approximations. Large and catastrophic claims. Reinsurance. Stochastic modelling with applications to (re)insurance. Undervisning Lectures combined with exercises. Continuous examination of problems/projects combined with written tests. Examination of seminars through oral presentation of written reports. Särskild behörighet 120 hp i teknik, naturvetenskap, företagsekonomi eller nationalekonomi vari ingår Sannolikhetslära 7,5 hp eller motsvarande samt En A. Examination PRO1, 4,5 högskolepoäng, betyg Godkänd (G) eller Väl Godkänd (VG), Fortlöpande examination/projekt SEM1, 3 högskolepoäng, betyg Godkänd (G), Seminarier Regler och anvisningar för examination i grundutbildningen vid Mälardalens högskola Betyg Godkänd (G) eller Väl Godkänd (VG). Miljöaspekter The course does not contain any specific environmental considerations. Litteratur Dickson, David C. M., Insurance Risk and Ruin. - Cambridge University Press, ISBN Gupta, A.K., Varga, T.,, An Introduction To Actuarial Mathematics. - Kluwer, ISBN The School of Education, Culture, and Communication may decide to change the above literature.

3 Statistisk inferensteori 7,5 högskolepoäng Methods of Statistical Inference Kurskod: MMA308 Utbildningsnivå: Grundnivå Ämne: Giltig fr.o.m. termin: vt09 Matematik/Tillämpad matematik. Kan även klassas som Nationalekonomi. Utbildningsområde: Naturvetenskap Huvudområde: Matematik/Tillämpad matematik med fördjupning G1F Fastställandedatum: Förändringsdatum: Syfte Statistical analysis of real market data has an important role in analytical finance and economics. The course aims to equip students with the skills required for statistical inference. The course presents the main concepts and methods of statistical inference, such as estimation, confidence intervals, hypothesis testing, regression analysis and analysis of variances. It is anticipated that Matlab and other software will be used throughout the course. Lärandemål At the end of the course the student is expected to be able to - describe and apply random sampling and statistical inference, in particular, the notions statistic, estimator, population, random sample, population distribution and sampling distribution. - describe point estimation, the main methods of estimation and the main properties of estimators, and apply them to data. - construct confidence intervals for unknown parameters. - describe and apply the main methods and concepts of hypotheses testing. - describe and apply the main methods and concepts of linear regression models. - describe and apply analysis of variance for a one-way layout. - describe and apply analysis of categorical data using Chi-square tests. Innehåll Review of Probability: probability, random variables, distributions, expectations, sampling distributions, sampling from normal distribution, Estimation: unbiased estimates and mean square error, selection of sample size, efficiency, consistency, sufficiency, minimum variance estimation, moment estimation, maximum likelihood estimation. Confidence Intervals: twosided and one-sided intervals, coverage probability, confidence intervals for parameters of normal distributions, pivots. Hypothesis Testing: error probabilities, likelihood ratio tests, tests for parameters of normal distribution, power of tests, Neyman-Pearson lemma, hypothesis testing and confidence intervals, p-values. Regression Analysis: linear models, estimation by least squares, inference for regression parameters, regression prediction. Analysis of Variance: one-way layout analysis, ANOVA tables, statistical inference for oneway layout. Undervisning

4 Lectures combined with exercises. Continuous examination of problems and projects combined with written tests. Work with and presentation of written reports. Särskild behörighet Sannolikhetslära 7,5 hp eller motsvarande. Examination PRO1, 3 högskolepoäng, Kontinuerlig examination SEM1, 1,5 högskolepoäng, Seminarium TEN1, 3 högskolepoäng, Skriftlig tentamen TEN2, 2 högskolepoäng, Test/tentamen. Test samt skriftlig och/eller muntlig tentamen för högre betyg än 3 G på kursen ÖVN1, 2 högskolepoäng, Obligatoriskt test ÖVN2, 2 högskolepoäng, Obligatoriskt test Regler och anvisningar för examination i grundutbildningen vid Mälardalens högskola Betyg Godkänd (G) eller Väl Godkänd (VG). Miljöaspekter The course does not contain any specific environmental considerations. Litteratur Litteraturlistan är preliminär till 15 arbetsdagar före terminens första kurstillfälle. Wackerly, D.D.,Mendenhall, W., Scheaffer. R.L.,, Mathematical Statistics with Applications. - Thomson Learning, 2008, 7 ed.. - ISBN

5 Portföljteori II 7,5 högskolepoäng Portfolio Theory II Kurskod: MMA705 Utbildningsnivå: Avancerad nivå Ämne: Giltig fr.o.m. termin: ht08 Matematik/Tillämpad matematik. Kan även klassas som Företagsekonomi, Nationalekonomi. Utbildningsområde: Naturvetenskap Huvudområde: Matematik/Tillämpad matematik med fördjupning A1N Fastställandedatum: Förändringsdatum: Syfte The course is a continuation of Portfolio Theory I. The Capital Asset Pricing Model (CAPM), and Arbitrage Pricing Theory (APT) will be surveyed in more detail during the semester. In addition, the students will study the valuation of assets; the inputs needed for construction of ex-ante optimal financial portfolios. Asset valuation will focus on equity instruments, using various techniques. Performance measurement and attribution will be examined through riskadjusted methods. Market timing and style investing will be discussed. Other topics surrounding portfolio allocation will include: Passive versus active management, market efficiency, value vs. growth, Roll's criticism, performance persistency, alternative investments, benchmarks, impact of transactions costs and peer groups. Risk management will be addressed via Value-at-Risk. There will be a project during the course. Lärandemål At the end of the course the student is expected to be able to - evaluate portfolio choices and conduct performance attribution. - account for and explain various structured fixed-income products and how they fit into portfolios. - elaborate on alternative asset s role in portfolios (Private equity and hedging strategies). - explain the residual income valuation model (RIV). - explain the discounted cash flow model (DCF). - use Treynor/Mazuy and Henriksson/Merton models in performance attribution. - use the Black-Litterman Model to calculate optimal portfolios. - manage an advanced project where the above mentioned abilities are used and make a well written report on the project. Innehåll Based on a mathematical and statistical setting; the course will explore the mechanics of portfolio theory. Regression analysis will be discussed (single and multifactor). Valuation (forecasting) will addressed via the discounted cash flow model (DCF), the dividend discount model (DDM), and the residual income valuation model (RIV). Evaluation of the investment management process and decomposition of portfolio performance will be studied via the Sharpe ratio, Jensen's alpha, the Treynor measure, Tracking-error, the Sortino ratio, and the information ratio. Market timing will be reviewed via the Treynor/Mazuy and Henriksson/Merton models. For portfolio construction and for calculation of covariance and

6 correlation matrices the emphasis is on matrix algebra and linear equations. At the end of the course students will approach current research in the field of finance; to see how predictability and the Black-Litterman model comes into play in portfolio construction. The course uses Excel for the valuation project Undervisning Lectures combined with exercises, two external lecturers and a valuation project. Särskild behörighet 120 hp i teknik, naturvetenskap, företagsekonomi eller nationalekonomi vari ingår Portföljteori I 7,5 hp eller motsvarande samt En A. Examination PRO1, 1,5 högskolepoäng, Projekt, kontinuerlig examination SEM1, 1,5 högskolepoäng, Seminarium TEN1, 6 högskolepoäng, Examination Regler och anvisningar för examination i grundutbildningen vid Mälardalens högskola Betyg Godkänd (G) eller Väl Godkänd (VG). Miljöaspekter The course does not contain any specific environmental considerations. Litteratur Litteraturlistan är preliminär till 15 arbetsdagar före terminens första kurstillfälle. Elton, Edwin J., Gruber, Martin J., Brown, Stephen J., Goetzmann, William N., Modern Portfolio Theory And Investment Analysis. - John Wiley And Sons Ltd, UK, 2006, 7 ed.. - ISBN The department for Mathematics and Physics may change the above literature