| source London School of Economics (X) |
level |
department |
The application of compound interest techniques to financial transactions. Describing how to use a generalised cash-flow model to describe financial transactions such as a zero coupon bond, a fixed interest security, an index-linked security, cash on deposit, an equity, an interest only loan, a repayment loan, an annuity certain and others. The time value of money using the concepts of compound interest and discounting. Accumulation of payments and present value of future payments. Expressing interest rates or discount rates in terms of different time periods. Real and money interest rates .The calculation of the present value and the accumulated value of a stream of equal or unequal payments using specified rates of interest and the net present value at a real (possibly variable) rate of interest, assuming a constant rate of inflation. Compound interest rate functions; definitions and use. Equations of value with certain and uncertain payments and receipts; conditions for existence of solution. Describe how a loan may be repaid by regular instalments of interest and capital; flat rates and annual effective rates. Calculation of a schedule of repayments under a loan and identification of the interest and capital components of annuity payments where the annuity is used to repay a loan for the case where annuity payments are made once per effective time period or p times per effective time period and identify the capital outstanding at any time. Discounted cash flow techniques and their use in investment project appraisal; internal rate of return, discounted payback period, money-weighted rate of return, time-weighted rate of return, linked internal rate of return. The investment and risk characteristics of fixed-interest Government borrowings, fixed-interest borrowing by other bodies, shares and other equity-type finance derivatives. The analysis of compound interest rate problems; the present value of payments from a fixed interest security where the coupon rate is constant and the security is redeemed in one instalment, upper and lower bounds for the present value of a fixed interest security that is redeemable on a single date within a given range at the option of the borrower, the running yield and the redemption yield from a fixed interest security, the present value or yield from an ordinary share and a property, given simple (but not necessarily constant) assumptions about the growth of dividends and rents, the solution of the equation of value for the real rate of interest implied by the equation in the presence of specified inflationary growth, the present value or real yield from an index-linked bond, the price of (or yield from) a fixed interest security where the investor is subject to deduction of income tax on coupon payments and redemption payments are subject to the deduction of capital gains tax,
Score: 6.5770254 Details | Listing | Web page
An introduction to stochastic processes with emphasis on life history analysis and actuarial applications. Principles of modelling; model selection, calibration, and testing; Stochastic processes and their classification into different types by time space, state space, and distributional properties; construction of stochastic processes from finite-dimensional distributions, processes with independent increments, Poisson processes and renewal processes and their applications in general insurance and risk theory, Markov processes, Markov chains and their applications in life insurance and general insurance, extensions to more general intensity-driven processes, counting processes, semi-Markov processes, stationary distributions. Determining transition probabilities and other conditional probabilities and expected values; Integral expressions, Kolmogorov differential equations, numerical solutions, simulation techniques. Survival models - the random life length approach and the Markov chain approach; survival function, conditional survival function, mortality intensity, some commonly used mortality laws. Statistical inference for life history data; Maximum likelihood estimation for parametric models, non-parametric methods (Kaplan-Meier and Nelson-Aalen), regression models for intensities including the semi-parametric Cox model and partial likelihood estimation; Various forms of censoring; The technique of occurrence-exposure rates and analytic graduation; Impact of the censoring scheme on the distribution of the estimators; Confidence regions and hypothesis testing.
Score: 6.5770254 Details | Listing | Web page
A solid coverage of the most important parts of the theory and application of regression models, generalised linear models and the analysis of variance. Analysis of variance models; factors, interactions, confounding. Multiple regression and regression diagnostics. Generalised linear models; the exponential family, the linear predictor, link functions, analysis of deviance, parameter estimation, deviance residuals. Model choice, fitting and validation. The use of a statistics package will be an integral part of the course. The computer workshops revise the theory and show how it can be applied to real datasets.
Score: 6.5770254 Details | Listing | Web page
A second course in stochastic processes and applications to insurance. Markov chains (discrete and continuous time), processes with jumps; Brownian motion and diffusions; Martingales; stochastic calculus; applications in insurance and finance. Content: Stochastic processes in discrete and continuous time; Markov chains: Markov property, Chapman-Kolmogorov equation, classification of states, stationary distribution, examples of infinite state space; filtrations and conditional expectation; discrete time martingales: martingale property, basic examples, exponential martingales, stopping theorem, applications to random walks; Poisson processes: counting processes, definition as counting process with independent and stationary increments, compensated Poisson process as martingale, distribution of number of events in a given time interval as well as inter-event times, compound Poisson process, application to ruin problem for the classical risk process via Gerber's martingale approach; Markov processes: Kolmogorov equations, solution of those in simple cases, stochastic semigroups, birth and death chains, health/sickness models, stationary distribution; Brownian motion: definition and basic properties, martingales related to Brownian motion, reflection principle, Ito-integral, Ito's formula with simple applications, linear stochastic differential equations for geometric Brownian motion and the Ornstein-Uhlenbeck process, first approach to change of measure techniques, application to Black-Scholes model. The items in the course content that also appear in the content of ST227 are covered here at greater depth. However, ST227 is not a pre-requisite for this course.
Score: 6.5770254 Details | Listing | Web page
The course introduces the student to the statistical analysis of time series data and simple models. What time series analysis can be useful for; autocorrelation; stationarity, basic time series models; AR, MA, ARMA; trend removal and seasonal adjustment; invertibility; spectral analysis; estimation; forecasting; introduction to financial time series and the ARCH model.
Score: 6.5770254 Details | Listing | Web page
An introduction to the theory and techniques of life insurance and pensions. Standard single life insurance products; endowments, annuities, and assurances. Extensions to multi-state policies and general benefits and premiums; two lives and more general multi-life functions including the joint life status and last survivor status, the multiple decrements model (competing risks), and the disability model, level and variable payments including increasing and decreasing assurances and annuities. Discrete and continuous time payments. Aggregate and select intensities. Actuarial notation for life contingencies and expected present values of standard products. Principles and techniques for determining premiums and reserves. The principle of equivalence. Thiele's differential equation and its generalizations. Variances and higher order moments of present values. Numerical methods. Woolhouse's formula relating present values in continuous and discrete time. Relationships between payments of annuity type and payments of assurance type. Notions of prospective and retrospective reserves and relationships between them. Administration expenses, gross premiums and gross reserves. With-profit contracts, surplus and dividends, various forms of bonus (cash bonus, terminal bonus, added benefits), interest rate guarantees, unit-linked insurance, defined benefits, defined contributions, salary-related benefits. Techniques for assessing profitability. Elements of population theory applied to life insurance. Heterogeneity, selection phenomena; intensities dependent on policy duration and state duration. Risk classification.
Score: 6.5770254 Details | Listing | Web page
An introduction to actuarial work in non-life insurance. Decision theory concepts: game theory, optimum strategies, decision functions, risk functions, the minimax criterion and the Bayes criterion. Loss distributions with and without limits and risk-sharing arrangements; suitable, moments and moment generating functions, the gamma, exponential, Pareto, generalised Pareto, normal, lognormal, Weibull, Burr and other distributions suitable for modelling individual and aggregate losses; statistical inference. Risk models involving frequency and severity distributions; the basic short-term contracts, moments, moment generating functions and other properties of compound distributions. Reinsurance treaties; proportional, excess of loss, stop-loss, deriving the distribution, moments, moment generating functions and other properties of the losses to the insurer and reinsurer under all the models above. Ruin theory for continuous and discrete models. Fundamental concepts of Bayesian statistics; Bayes theorem, prior distributions, posterior distributions, conjugate prior distributions, loss functions, Bayesian estimators. Credibility theory; Bayesian models. Experience rating models and applications. Claims reserving: run-off triangles. Monte-Carlo simulation and applications in insurance.
Score: 6.5770254 Details | Listing | Web page
The main ideas and applications of market research techniques. Problem formulation and research designs for market and opinion research. Random sampling and statistical inference. Quota sampling. Survey stages and sources of error. Data collection methods. Attitude measurement. Market models, advertising and public opinion research. The analysis of market research data.
Score: 6.5770254 Details | Listing | Web page
Main ideas and techniques used in marketing and opinion research. Statistical methods applied to market research data. ST327.1 Research Methods: Problem formulation and research designs for market and opinion research. Sample theory and methods. Survey stages and sources of error. Data collection methods. Attitude measurement. Market models, advertising and public opinion research. The analysis of market research data using statistical methods of cluster analysis, factor analysis, structural equation modeling and latent class analysis. ST327.2 Case Studies: Students use the information and techniques gained from ST327.1 to carry out a co-operative Marketing Case Study. Individual write up of the Case Study forms part of the assessment.
Score: 6.5770254 Details | Listing | Web page
Applications of stochastic processes and actuarial models in finance. Utility theory. Stochastic dominance and portfolio selection. Measures of investment risk. Mean-variance portfolio theory. Single and multifactor models. Asset liability modelling for actuaries. The Capital Asset Pricing Model. The efficient market hypothesis. Stochastic models for security prices and estimating their parameters. The term structure of interest rates: the Vasicek, the Cox-Ingersoll-Ross and other models. Option pricing: general framework in discrete and continuous time, the Black-Scholes analysis and numerical procedures (binomial models and Cox-Ross-Rubinstein models).
Score: 6.5770254 Details | Listing | Web page
The fundamentals of the theory of decision analysis and its use in Bayesian statistics. Topics covered are the foundations of decision theory and Bayesian statistical methods with applications. ST331.1 Fundamentals of Decision Theory (Dr J Howard). The normative theory of subjective probability and expected utility. ST331.2 Bayesian Statistical Methods (Professor H Wynn). General discussion of the Bayes approach and comparison with other approaches to statistical inference. Applications to some statistical problems.
Score: 6.5770254 Details | Listing | Web page
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