One of the most relevant problems in actuarial mathematics is the question of calculating the premium, i.e the price to be paid to insurance companies to provide coverage insurance. In this thesis we examine the most modern premium calculation principles, in order to consider the catastrophic risks. We will use as a model for the risk the cumulative claim: S = X1 + X2 +...+ XN, where Xi are nonnegative random variable characterized by flat and thick tails and thin or fat tailed, independent and identically distributed and the random variable N represents the number of claims, independent of Xi. Accordingly, the thesis is structured as follows: in Chapter 1 we will examine main premium calculation, including Wang principle and Esscher principle. We will also examine some desirable properties of these principles and after we will produce an application of a transformation of comonotonic and exponential tilting to the principles of Wang and Esscher premium calculation, showing how the results occur some fundamental calculation premium properties. In Chapter 2 we will study the insurability of catastrophe risks, including earthquake risk, focusing on seismicity problem in Italy. We will estimate moreover an insurance premium by applying the Wang calculation principle at frequencies of Italian earthquakes in a large time interval (217 BC-2002). Finally, in Chapter 3 we will examine the alternative management of catastrophic events, i.e a set of alternative risk transfer instead of traditional insurance. Among these solutions, we will focus on securitization transactions, i.e. the securitization of insurance risks, particularly on Catastrophe Bonds (Cat Bonds) CAT bonds are innovative financial instruments that have an important role in the financing of mega-catastrophes and other losses. One of the reason of wide use of these financial solutions is the increasing need of insurance for catastrophic risks, due to several factors: increased population density, greater concentration of valuables in small areas, finally the increasing number of natural disasters. Moreover, financial resourses of insurance companies regularly faced with severe capacity limits for catastrophic exposures. It should be underlined that these financial products are not a substitute for reinsurance, but they are complementary, for a better management of catastrophic events.

### Il calcolo del premio assicurativo per gli eventi catastrofali

#### Abstract

One of the most relevant problems in actuarial mathematics is the question of calculating the premium, i.e the price to be paid to insurance companies to provide coverage insurance. In this thesis we examine the most modern premium calculation principles, in order to consider the catastrophic risks. We will use as a model for the risk the cumulative claim: S = X1 + X2 +...+ XN, where Xi are nonnegative random variable characterized by flat and thick tails and thin or fat tailed, independent and identically distributed and the random variable N represents the number of claims, independent of Xi. Accordingly, the thesis is structured as follows: in Chapter 1 we will examine main premium calculation, including Wang principle and Esscher principle. We will also examine some desirable properties of these principles and after we will produce an application of a transformation of comonotonic and exponential tilting to the principles of Wang and Esscher premium calculation, showing how the results occur some fundamental calculation premium properties. In Chapter 2 we will study the insurability of catastrophe risks, including earthquake risk, focusing on seismicity problem in Italy. We will estimate moreover an insurance premium by applying the Wang calculation principle at frequencies of Italian earthquakes in a large time interval (217 BC-2002). Finally, in Chapter 3 we will examine the alternative management of catastrophic events, i.e a set of alternative risk transfer instead of traditional insurance. Among these solutions, we will focus on securitization transactions, i.e. the securitization of insurance risks, particularly on Catastrophe Bonds (Cat Bonds) CAT bonds are innovative financial instruments that have an important role in the financing of mega-catastrophes and other losses. One of the reason of wide use of these financial solutions is the increasing need of insurance for catastrophic risks, due to several factors: increased population density, greater concentration of valuables in small areas, finally the increasing number of natural disasters. Moreover, financial resourses of insurance companies regularly faced with severe capacity limits for catastrophic exposures. It should be underlined that these financial products are not a substitute for reinsurance, but they are complementary, for a better management of catastrophic events.
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The calculation of insurance premium for catastrophic events
5-mar-2010
Aversa, Monica
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11695/66222`