Contributions published at Finance and Insurance (Cosimo Munari)

Catastrophe (CAT) bonds are nancial contracts whose value is primarily driven by insurance-linked variables. Roughly speaking, the payo of a CAT bond is contingent on an underlying index not exceeding a given threshold, known as the attachment point. Should this threshold be exceeded, the CAT bond investor loses the notional amount fully or partially and the CAT bond is said to be triggered. The index movements are typically driven by the occurrence and economic impact of natural disasters. The events on which CAT bonds are based can be classied as low frequency and high severity; for this reason, they can be analyzed and predicted in a statistically optimal manner using Extreme Value Theory (EVT).

This thesis investigates the portfolio optimization process with Value at Risk. Following the Mean-Variance framework developed by Markowitz (1952), we propose the Mean-VaR optimized portfolio and reveal the working mechanism of budget constraint, no-shorting constraint and risk constraint for our portfolio. In the mathematical analysis, the Lagrange multiplier and rst order derivative will be applied. In the setting with one bond and one stock, we nd that an increase in the stock's expected return increases the expected return of the portfolio and increase the weight of the stock investment. However, increasing the stock's VaR will decrease the portfolio's expected return and the investment amount of the stock. Increasing the bond return decreases the weight of the bond investment when the bond return is still smaller than the stock return, but after the bond return is bigger than the stock return, there is a jump where the bond investment's weight remains at 100% whilst the stock's weight keeps at 0. After expanding our research to a two-stock setting, we nd increasing the correlation parameter,  decreases the weight of riskier assets and increase the weight of less risky assets. In addition, the budget constraint will only aect the investment amount rather than the investment weights. Consequently, the expected return of the portfolio will also decrease when we increase the assets' correlation. From this perspective, diversication can improve the performance of our portfolio. We compare the Mean-Variance portfolio and the Mean-VaR portfolio with four US stocks, Google, Walmart, P&G and GE. By simulating the allocation of the portfolio, we nd that the Mean-VaR portfolio is more conservative than the Mean-Variance portfolio, as the Mean-VaR portfolio shows a narrower ecient frontier. After introducing a risk-free bond to the portfolio, we nd a higher risk-free rate can lead to a higher overall expected return. We recommend using a moving average method for VaR estimation in long-term investment, as it is more exible and able to capture the recent return change. Ultimately, the primary task for the Mean-VaR portfolio is to set up a reasonable risk constraint level and diversication can be benecial to investors.

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A callable bond is a type of bond that allows the issuer of the bond to retain the privilege of redeeming the bond at some point before the bond reaches its date of maturity. In other words, on the call dates, the issuer has the right, but not the obligation, to buy back the bonds from the bond holders at a dened call price. Practically speaking, the bonds are not really bought and held by the issuer but are instead cancelled immediately. From the above description, we could see that the callable bond can be viewed as giving the bond issuer a call option on the bond. And this is very important for the pricing of callable bond. More details will be discussed in the following chapters for callable bond pricing under dierent interest rate models. Insurance company and investors usually use callable bond to make prot and hedge risk. Callable bonds usually have a higher yield, partly because of the fact that callable bonds allow the investors to have eectively sold an option to the issuer, and partly because of the smaller market size and the fact that issuers want to make the callable bonds more attractive to investors who otherwise might not want to invest in callable bonds. Insurance rms tend to have a large diversied portfolio of assets and bonds in order to hedge the investment risk.Due to the property of a higher yield and other properties, callable bond is playing an important role in helping the investors to establish an opti- mized portfolio. In this paper we are interested in the theoretical price of callable bond under various of interest rate models: CIR model, Vasecik model and Hull-White model. Besides, we will also study the risks that will in uence the callable bond price under various models. We will mainly focus on the zero coupon callable bond pricing and risk management, since the more complicated callable bond types can be viewed as derivatives of zero coupon callable bond. 3

I first make a thorough review of the academic literature dedicated to life insurance and outline the evolution of scientific thought since the mid-1960s. Afterwards, I show how the European life insurance legislation evolved over the same period. Additionally, I explore how the life market developed during and after the last financial crisis. Finally, I use the econometrics of panel data on two samples of ten EU member states in the period 1995-2015 to determine the life insurance demand drivers common to Eastern and Western European countries. I find evidence that the drivers in Eastern Europe are different from those observed in Western Europe.

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The objective of this thesis is to provide a comprehensive analysis of Insurance-Linked Securities as an investment opportunity, whereas the optimal allocation to ILS is investigated for standard portfolios of professional/qualified investors. Given the heavy-tailed risks underlying ILS products, the first part of the study conducts a quantification of the diversification potential of ILS as measured by tail risk metrics such as Value at Risk, Expected Shortfall and risk measures based on Benchmark Loss Distributions. Moreover, from a Portfolio Selection perspective, the analysis is complemented with an investigation of the composition of optimal portfolios in a Markowitz-type setting, where the variance is replaced by one of the above risk metrics. The findings reveal that in most of the cases, a high allocation to Insurance-Linked Strategies in detriment of other Alternative Investments leads to a better risk-reward pattern. Nevertheless, for high levels of confidence as well as under risk measures based on benchmark loss distributions, the optimal allocation to Insurance-Linked Securities both from a risk management and a portfolio selection perspective is reduced by half .

Within the context of capital adequacy, we study comonotonicity of risk measures in terms of the primitives of the theory: acceptance sets and eligible, or reference, assets. We show that comonotonicity cannot be characterized by the properties of the acceptance set alone and heavily depends on the choice of the eligible asset. In fact, in many important cases, comonotonicity is only compatible with risk-free eligible assets. The incompatibility with risky eligible assets is systematic whenever the acceptability criterion is based on Value-at-Risk or any convex distortion risk measure such as Expected Shortfall. These findings qualify and arguably call for a critical appraisal of the meaning and the role of comonotonicity within a capital adequacy context.

We provide a variety of results for quasiconvex, law-invariant functionals defined on a general Orlicz space, which extend well-known results from the setting of bounded random variables. First, we show that Delbaen’s representation of convex functionals with the Fatou property, which fails in a general Orlicz space, can always be achieved under the assumption of law-invariance. Second, we identify the class of Orlicz spaces where the characterization of the Fatou property in terms of norm-lower semicontinuity by Jouini, Schachermayer and Touzi continues to hold. Third, we extend Kusuoka’s representation to a general Orlicz space. Finally, we prove a version of the extension result by Filipović and Svindland by replacing norm-lower semicontinuity with the (generally non-equivalent) Fatou property. Our results have natural applications to the theory of risk measures.

We show that for a convex solid set of positive random variables to be tight, or equivalently bounded in probability, it is necessary and sufficient to be is radially bounded, i.e. that every ray passing through one of its elements eventually leaves the set. The result is motivated by problems arising in mathematical finance.

The use of gender as a risk factor in the calculation of premiums and benefits has been a deep-rooted actuarial practice. Statistical evidence demonstrates systematic differences in the loss frequency in terms of mortality rate and traffic accidents between men and women, which are reflected in their life and motor insurance premiums. Nevertheless, on 1 March 2011 the European Court of Justice decided to prohibit gender-based pricing in the insurance sector since it was deemed to go against the principle of equal treatment between individuals. This research provides a comprehensive discussion on the current use of gender as a risk factor in insurance pricing and the potential economical implications of unisex pricing within a Swiss context. The first parts focus on the theoretical and legal aspects of insurance pricing. There then follows a thorough discussion on the current practice with regard to the use of gender and the practical application of the European Court of Justice Judgment. This research outlines the economic inefficiencies of imposing unisex pricing by investigating the case of term life insurance and motor insurance in Switzerland.