Actuarial Mathematics - I - PSAU

Theory of Interest & Financial Functions:Time Value of Money: Simple interest, compound interest, nominal vs. effective interest rates, and discount factors (\(v = \frac{1}{1+i}\)).Annuities-Certain: Present and accumulated values of discrete and continuous annuities (annuities due, immediate annuities, and perpetuities).Amortization and Yields: Loan repayment schedules, outstanding loan balances, and yield rate determination.Survival Models & Life Tables:Future Lifetime Distributions: Continuous and discrete random variables representing the remaining lifetime of a person aged x (\(T_{x}\) and \(K_{x}\)).Actuarial Notation: Standard survival functions (\(p_{x}\)) and mortality functions (\(q_{x}\)), along with force of mortality (\(\mu _{x}\)).Life Tables: Using deterministic life tables to compute conditional survival probabilities across specific age intervals.Analytical Laws of Mortality: Classical fractional age assumptions (Uniform Distribution of Deaths - UDD, Constant Force of Mortality).Life Insurance Products (Long-Term Models):Present Value Random Variables: Modeling the present value of benefits paid out upon death.Insurance Types: Term life insurance, whole life insurance, and endowment insurance.Net Single Premiums: Calculating the Expected Present Value (EPV) of continuous and discrete life insurance contracts.Life Annuities:Continuous & Discrete Life Annuities: Evaluating the EPV of income streams paid conditionally on survival (e.g., whole life annuities, temporary annuities).Premium Principles: Setting up the "Loss at Issue" random variable and calculating net annual benefit premiums using the equivalence principle.