Actuarial Mathematics -II - PSAU

Gross Premiums & Expense Loading:Moving beyond net premiums to account for expenses (taxes, commissions, administrative costs).Formulating the Gross Loss-at-Issue random variable and calculating gross premiums using the equivalence principle.Reserving & Policy Values:Net Premium Reserves: Calculating retrospective and prospective reserves for standard life insurance and annuity contracts.Recursion Formulas: Analyzing how reserves change from year to year (Thiele's Differential Equation for continuous models, standard recursion for discrete models).Expense Reserves: Accounting for modified reserve systems (e.g., Full Preliminary Term method) to handle high first-year expenses.Multiple Life Contingencies (Joint Life & Last Survivor Status):Joint Life Status (xy): Models that fail upon the first death among a pair or group of lives.Last Survivor Status (\(\overline{xy}\)): Models that fail only after all individuals in the group have died.Contingent Probabilities: Calculating specific probabilities and Expected Present Values (EPV) for insurances paid only if individual x dies before individual y.Multiple Decrement Models:Analyzing systems where a policy can terminate due to more than one cause (e.g., death, accidental death, disability, or voluntary policy lapse).Differentiating between associated single decrement tables (net probabilities) and multiple decrement tables (gross, dependent probabilities).Pension Mathematics & Multi-State Models:Formulating career-average and final-salary pension schemes.Using Markov chains and multi-state transition intensities to model health, sickness, disability, and retirement transitions.