Insurance Risks. Risk measures. Premium principles. Retention and reinsurance.
Balances of insurance companies.
Optimal management criteria.
Profitability in motor insurance bonus-malus systems. Profitability and mutuality with direct indemnification in motor insurance.
Evaluations fraudolence: strategic and inferential aspects.
Methodological bases for stochastic simulation.
L. Vannucci, Teoria del rischio e tecniche attuariali contro i danni, Pitagora Editrice,
KNOWLEDGE: to know how to identify and measure the riskiness of economic activities with particular reference to insurance against damages.
SKILLS: to solve the problems related to the management of insurance risk processes with the appropriate modeling and the appropriate analysis of these processes.
ACQUISIBLE CAPACITIES: to manage situations of insurance risk, reconciling theoretical modeling and empirical evidence.
PROBABILITY AND MATHEMATICS FOR STATISTICS
Frontal lecture with the aid of computational tools
Type of Assessment
Written test. The oral exam is at the request of the student, if the assessment of the written test is not considered adequate.
1. STOCHASTIC MODELS FOR THE DESCRIPTION OF THE RISKS RELATED TO THE INSURANCE ACTIVITIES OF ELEMENTARY BRANCHES 1.1 Classification of no-life insurance 1.2 No-life insurance branches
1.3 Insurance reimbursement: number of claims, amount of individual cost, total cost 1.4 Models for the random number of claims 1.5 Total insurance reimbursement
2. RISK MEASUREMENT CRITERIA AND PRINCIPLES OF DETERMINATION OF INSURANCE PREMIUMS 2.1 Fair award, pure (or net) premium and tariff premium 2.2 Properties of the criteria for calculating the premium 2.3 Experience based awards 2.4 Prizes and credibility theory 2.5 Awards with modulated uploads on the entities of the possible compensation: stratified insurance (layer)
3. RE-INSURANCE AND RISK RETENTION POLICIES 3.1 Co-insurance and reinsurance 3.2 Relationships, treaties, forms of reinsurance 3.3 Particular forms of reinsurance 3.4 Retrocessions of reinsurance 3.5 Reinsurance premiums and expediency to reinsure
4. BUDGETS OF INSURANCE COMPANIES 4.1 Peculiarities in the administration of insurance companies 4.2 Balance sheet, income statement and cash flow statement 4.3 An example of accounting construction of successive balance sheets
5. RESERVES IN NO-LIFE DAMAGES 5.1 Statistical models for estimating the claims reserve 5.2 Estimate of the claims reserve with the separation method 5.3 Reserve of equilibrium
6 MANAGEMENT CRITERIA 6.1 Some analytical results on the probability of ruin 6.2 Probability of ruin in limited time 6.3 Average duration of the activity before ruin 6.4 Maximizing the expected current value of the economic result 6.5 Extensions to risk processes with non-independent increments 6.6 Competition between companies
7. DETERMINATION OF THE REMUNERATION CONNECTED WITH THE MANAGEMENT OF THE CAR CIVIL LIABILITY INSURANCE IN A BONUS-MALUS SYSTEM 7.1 The standard Italian Bonus-Malus system 7.2 Moments of the present values of premiums and returns on a limited horizon 7.3 Moments of the present values of premiums and returns on an unlimited horizon
8. PROFITABILITY, MUTUALITY AND DIRECT INDEMNITY IN CAR CIVIL LIABILITY INSURANCE: A MODEL FOR ACTUARIAL ASSESSMENTS 8.1 Recalls on the new legislation 8.2 Premise for the construction of a model for CARD claims 8.4 Evaluations for the CARD-CID type 8.5 Evaluations for the CARD-CTT type
9. FRAUDULENCE IN CAR CIVIL LIABILITY INSURANCE: STRATEGIC ASPECTS AND INFERENTIAL ASPECTS 9.1 Introduction 9.2 On the modeling of the strategic behavior of economic agents 9.4 Game models related to fraudulent behavior 9.5. An econometric model for moral hazard ex post 9.6 Estimate of the degree of fraudulence from individual data 9.7 A specific example
10. METHODOLOGICAL BASIS AND METHOD OF USE OF SIMULATION IN NON-LIFE DAMAGES 10.1 Generation of random numbers 10.2. Simulation of random variables 10.3. Simulation results and inference on the quantities of interest 10.4 Different approaches to using the simulation 10.5 Examples