Exam ALTAM – Advanced Long-Term Actuarial Mathematics

7 个单元 · 36 个章节

免费 Exam ALTAM – Advanced Long-Term Actuarial Mathematics 学习笔记，适合 SOA (Society of Actuaries) 学生。每个章节都覆盖一个重点主题，并附例题与可延伸到 thinka app 的练习提示。

Survival Models for Contingent Cash Flows

Mortality curves and heterogeneity in mortality
Markov multiple state models for life and long-term health benefits and CCRCs
Assumptions underlying Markov multiple state models
Kolmogorov's forward equations for continuous-time Markov models
State-dependent probabilities for continuous-time Markov models
Chapman-Kolmogorov equations for discrete-time transition probabilities
Multiple decrement tables and single decrement models
Maximum likelihood estimates of transition intensities and probabilities
Confidence intervals for transition intensity estimators

Premium and Policy Valuation for Long-Term State-Dependent Coverages

State-dependent insurance and annuity present value random variables
Two-term and three-term Woolhouse approximations
Premiums for state-dependent coverages by the equivalence principle
Policy values for state-dependent coverages
Thiele's differential equation

Joint Life Insurance and Annuities

Modelling joint-life mortality: time-to-status-failure and multiple state models
Dependence of future lifetimes in joint life models
Premiums for insurance and annuities on joint lives
Policy values for insurance and annuities on joint lives

Profit Analysis

Expected profit and actual profit
Analysis of gains by source
Profit signature, profit vector, NPV, IRR, profit margin, and discounted payback period
Premiums based on a specified profit objective
Reserves using profit testing

Pension Plans and Retirement Benefits

Replacement ratios for DC and DB plans (FAS, CAE, CARE)
Required contribution rate for a DC plan
Service table and salary scale functions
Accrued benefits for a DB plan, including early exit
Actuarial accrued liability and normal cost: PUC and TUC methods

Universal Life Insurance

Account values and benefits under Type A and Type B Universal Life policies
Reserves for no-lapse guarantees
Deterministic profit testing for Universal Life insurance

Embedded Options in Life Insurance and Annuity Products

Payoffs under embedded guarantees: GMDB, GMMB, GMIB, and GMWB
Valuing embedded guarantees using the Black-Scholes model
Replicating portfolios via delta-hedging
Costs of discrete-time rebalancing
Profit testing for equity-linked life insurance cash flows

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