Insurance Mathematics - NU

1. Foundation of Insurance RisksUtility Theory: Modeling consumer risk aversion and calculating the maximum premium an insured is willing to pay versus the minimum an insurer can accept.Premium Loading Principles: Designing commercial premiums by adding risk, safety, and administrative load factors to the pure mathematical risk cost.2. Life Insurance Mathematics (Long-Term Contingencies)Survival Probabilities: Developing random variable models for expected human lifespan using mortality laws (e.g., Gompertz-Makeham).Benefit Valuation: Finding the expected present value for whole life, term, and endowment insurance contracts.Annuity Systems: Modeling retirement and pension cash streams contingent on survival.Prospective Reserves: Calculating the funds an insurer must hold to back future claim obligations using net and gross methods.3. Non-Life Insurance Mathematics (Short-Term & Property)Collective Risk Models: Structuring aggregate portfolio loss distributions by combining claim frequency (Poisson) and claim severity (Pareto/Gamma).Ruins Theory: Using continuous stochastic processes to calculate ruin probability—the likelihood that an insurance company's claims will exceed its financial reserves.Reinsurance Structures: Modeling risk-sharing mathematics between primary insurers and reinsurers via Quota-Share or Excess-of-Loss treaties