# Università degli Studi di Napoli "Parthenope"

## Teaching schedule

2017/2018
Belonging course:
Disciplinary sector:
MATHEMATICAL METHODS OF ECONOMY, FINANCE AND ACTUARIAL SCIENCES (SECS-S/06)
Language:
Italian
Credits:
6
Year of study:
3
Teachers:
Cycle:
Second semester
Hours of front activity:
48

Italian

### Course description

The course aims to provide the methodologies for the formalization and evaluation of life insurance contracts; to introduce the construction of models for measuring premiums, technical reserves and the Solvency Capital Requirement (SCR) under the Solvency II regulation.

The acquired knowledge allows the student to understand and critically assess the problem of defining, measuring and controlling risk in life insurance; the control of quantitative techniques for pricing a policy, for the calculation of technical reserves and the SCR in the standard formula. Furthermore, the student will acquire knowledge of the sector jargon both in Italian and English.

Ability to apply probabilistic and statistical techniques to insurance; knowledge of the relevant databases for the management of typical insurance risks in the Solvency II framework; mathematical tools for evaluating technical provisions of traditional and profit-sharing policies. Skills for informed setting and assessing management policies for ensuring solvency; ability to critically read and evaluate the scientific literature.

### Prerequisites

Fundamentals of probability, stochastic processes, mathematical models of financial markets and theory of decisions under uncertainty.

### Syllabus

The Solvency II regulation. Life insurance policies, some examples.
I Foundation of actuarial mathematics (8 hours)
Probabilistic models for life expectancy and standard actuarial notations
Classification according to benefits,
Classification according to premia,
Reserving,
III – Profit-sharing policies
The revaluation formula; the embedded options.
Mark-to-market evaluation.
Actuarial and financial risk drivers.
Actuarial and financial components of the valuation.
Probability distribution and the Solvency Capital Requirement; the standard formula.

The Solvency II regulation. Life insurance policies, some examples.
I Foundation of actuarial mathematics (8 hours)
Probabilistic models for life expectancy and standard actuarial notations
Classification according to benefits,
Classification according to premia,
Reserving,
III – Profit-sharing policies
The revaluation formula; the embedded options.
Mark-to-market evaluation.
Actuarial and financial risk drivers.
Actuarial and financial components of the valuation.
Probability distribution and the Solvency Capital Requirement; the standard formula.

### Teaching Methods

Frontal lections. Lab activities to develop Excel-based software procedures to solve financial problems.

### Textbooks

Gerber, H.U., Life Insurance Mathematics, Springer, 2011,
Castellani, G., De Felice, M., Moriconi, F., Manuale di finanza III. Modelli stocastici e contratti derivati, Bologna, Il Mulino, 2006.
De Felice, M., Moriconi, F., Finanza dell'assicurazione sulla vita. Principi per l'asset-liability management per la misurazione dell'embedded value,Giornale dell'Istituto Italiano degli Attuari, LXV(2002), 1-2.
De Felice, M., Moriconi, F.,Market Based Tools for Managing the Life Insurance Company, Astin Bulletin, 35(2005), 1.
Gerber, H.U., Life Insurance Mathematics, Springer, 2011,
Castellani, G., De Felice, M., Moriconi, F., Manuale di finanza III. Modelli stocastici e contratti derivati, Bologna, Il Mulino, 2006.
De Felice, M., Moriconi, F., Finanza dell'assicurazione sulla vita. Principi per l'asset-liability management per la misurazione dell'embedded value,Giornale dell'Istituto Italiano degli Attuari, LXV(2002), 1-2.
De Felice, M., Moriconi, F.,Market Based Tools for Managing the Life Insurance Company, Astin Bulletin, 35(2005), 1.
Pacati, C., Appunti delle lezioni di matematica attuariale delle assicurazioni sulla vita, 2013. Disponibile all'indirizzo: https://drive.google.com/file/d/1Bp9UuixR5_8E-XZmyY5i_zq1qAH_itFU/view
Pitacco, E., Matematica e tecnica attuariale delle assicurazione sulla durata di vita, LINT, 2008.

### Learning assessment

The achievement of the learning purposes will be evaluated by means of a written test aimed at verifying the operational abilities and an oral interview aimed at understanding the degree of theoretical knowledge and the communication skills of the student. In particular, students will have to take a 90-minute test, using Excel, consisting of three exercises related to the application of formulas and algorithms for: 1. calculation of premiums and technical reserves of traditional policies; 2. mark-to-market valuation of profit-sharing policies; 3. valuation of the SCR in the standard formula. The exercise 1 is worth 12 points, the exercises 2. and 3. are worth 9 points each. The admission to the oral interview requires at least a score of 8 for exercise 1., and at least 5 for each of the exercises 2. and 3.
The oral examination consists of two questions that focus on the theoretical issues related to the evaluation of the characteristic quantities of a life insurance policy: pricing, risk and reserve. For each question the maximum score is 15; the student must attain at least 9 points for each of the two questions.
The grade will be the average of the scores of the two tests.