CM1 – Actuarial Mathematics for Modelling
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IFoA (Institute and Faculty of Actuaries) の学習者向けの無料CM1 – Actuarial Mathematics for Modelling学習ノート。各章のリンクから、要点・例題・練習問題への導線にアクセスできます。
Theory of interest rates
Interest and discount rates, and rate conversions
Simple and compound interest, discounting a single payment
Force of interest varying with time
Real and money rates: allowing for inflation
Cashflow models of financial instruments and insurance contracts
Level annuities and accumulations: annual, pthly and continuous
Deferred, increasing and varying annuities
Present and accumulated values of general cashflow streams
Term structure, duration and immunisation
Term structure of interest rates and its determinants
Spot rates and forward rates, discrete and continuous
Par yield and yield to maturity
Duration and convexity of a cashflow sequence
Redington's conditions and immunisation of liabilities
Equation of value and its applications
The equation of value: certain and uncertain payments
Loan schedules, capital and interest components, APR
Bond pricing and yields with income tax and capital gains tax
Running yield, redemption yield and index-linked bonds
Optional redemption dates: bounds on present value
Valuing ordinary shares and property with growing income
Project appraisal: NPV, IRR and payback periods
Decrement and multiple life models
Life contingencies: contracts and life tables
Assurance and annuity contract types and their cashflows
With-profits, unit-linked and accumulating with-profits contracts
Life table functions and select mortality
Survival and death probabilities, deferred and select forms
Assurance and annuity factors, including continuous and pthly forms
Relationships between assurance and annuity functions
Pricing and reserving
Means, variances and multiple life functions
Expected present value and variance of benefit payments
Premium and benefit payment patterns in EPV formulae
Expected accumulations under assurance and annuity contracts
Joint life and last survivor functions
Two-life functions dependent on a fixed term as well as age
Multiple state and multiple decrement models
Multiple-state Markov models: forces and probabilities of transition
Health insurance premium and benefit structures
EPVs of cashflows contingent on multiple transitions
Multiple decrement tables and their construction
Dependent probabilities and forces of transition
Premiums and reserves
The gross future loss random variable
Gross premiums by the equivalence principle, with expenses
Prospective and retrospective reserves and their equivalence
Recursive relationships between successive reserves
Net premiums and net premium valuation
Death strain at risk and mortality profit
Profit testing and cashflow projection
Projecting expected cashflows with multiple decrements
Profit vector, profit signature, NPV and profit margin
Using a profit test to price a contract
Unit-linked contracts: unit and non-unit fund projections
Zeroising negative cashflows with non-unit reserves
Reserves within a profit test and their effect on profit
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