30 mai 2016

CTEbased capital allocation for some multivariate models
Raluca Vernic (Ovidius University, Constanta, Romania)
11:0012:00, salle Extranef 126
Plus d'informationAn insurance company must be able not only to evaluate the total appropriate amount of capital needed to cover its aggregate loss, but also to solve the capital allocation problem, which consists in fairly allocating this capital among its various lines of business. Risk measures are wellknown tools used for this purpose, and one of the most popular such risk measure is the TailValueatRisk, called Conditional Tail Expectation (CTE) in the continuous case. This risk measure describes the expected amount of risk that can be experienced given that the risk exceeds a threshold value, thus providing an important measure of the righttail risk. In this talk, we present CTE formulas for the multivariate skewnormal distribution, for the multivariate Pareto distribution and for Sarmanov’s class of distributions. In the case of the multivariate Pareto distribution, a special technique based on recursions is developed. Moreover, as a numerical illustration, we also present the results of a study on a set of bivariate real data from auto insurance (third party liability and bodily injury). In this study, we considered several continuous bivariate distributions and, looking for a better fit, we also considered a bivariate nonparametric transformed kernel density. Therefore, numerical results on the real data are discussed and compared, and some difficulties in implementing the theoretical formulas are underlined.

10 juin 2016

Rafal Kulik (University of Ottawa, Canada)
11:0012:00, salle Extranef 110

21 juin 2016

Joint with EPFL: Asymmetric Information in Automobile Insurance: Evidence from Driving Behavior
Alexander Mürmann (Vienna University of Economics and Business)
12:0013:00, salle Extranef 126
Plus d'informationBased on a unique data set of driving behavior we find direct evidence that private information has significant effects on contract choice and risk in automobile insurance. The number of car rides and the relative distance driven on weekends are significant risk factors. While the number of car rides and average speeding are negatively related to the level of liability coverage, the number of car rides and the relative distance driven at night are positively related to the level of firstparty coverage. These results indicate multiple and counteracting effects of private information based on risk preferences and driving behavior.

4 juillet 2016

Optimal Dividend payout with Risk Sensitive Preferences
Nicole Baeuerle (Karlsruhe Institute of Technology, Germany)
14:0015:00, salle Extranef 126
Plus d'informationWe consider a discrete time dividend problem with risk sensitive preferences for the dividends. This leads to a nonexpected recursive utility of the dividends which is constructed with the help of the exponential premium principle. Models like this have the advantage that the variability of the dividends is also taken into account and risk aversion can be introduced. This kind of research has been motivated in a remark in Gerber and Shiu (2004). We develop the theoretical tools in order to solve these kind of optimization problems for finite and infinite time horizons. Moreover we prove that even in this general setting, the optimal dividend policy is a band policy. We also showthat the policy improvement algorithm can be used to compute the optimal policy and the corresponding value function. An explicit example is given where we can show that a barrier policy is optimal. Finally some surprising numerical examples are provided where we discuss the influence of the risk sensitive parameter on the optimal dividend policy.

6 juillet 2016

Periodic capital injections based on the claim frequency
JK Woo (The University of Hong Kong)
14:0015:00, salle Extranef 126
Plus d'informationThe literature on the various risk models related to capital injection problem has grown considerably in recent years. Most proposed models implicitly assume that the decision on capital injections are made according to the continuous monitoring of the insurer's surplus. However, it is costly and unrealistic in practice. Therefore, in this talk we propose the periodic capital injection strategy in which surplus level is recovered to a predetermined minimum solvency level z whenever it is below level z after every "N"th claim. We also assume that an immediate capital injection with the penalty involving the deficit is required when ruin occurs. Furthermore, with the aid of the discounted density of surplus at claim instants, higher order ordinary differential equation with an integraltype boundary condition is derived for the expected discounted capital injection when the claim size distribution is a combination of exponentials. Lastly, some numerical examples are presented to illustrate how the strategy based on "N" has impact on the expected discounted capital injection amount. This is a joint work with Ran Xu.

6 juillet 2016

On a risk model with periodic capital injections at Erlang intervals
Eric C.K. Cheung (The University of Hong Kong)
15:0016:00, salle Extranef 126
Plus d'informationThe analysis of capital injection strategy in the literature of insurance risk models (e.g. Pafumi (1998), and Dickson and Waters (2004)) typically assumes that whenever the surplus becomes negative, the amount of shortfall is injected so that the company can continue its business forever. Recently, Nie et al. (2011) has proposed a more realistic model in which capital is immediately injected to restore the surplus level to a positive level b when the surplus falls between zero and b, and the insurer is still subject to a positive ruin probability. Inspired by the idea of randomized observations in Albrecher et al. (2011), we further generalize Nie et al. (2011)'s model by assuming that capital injections are only allowed at a sequence of time points whose intervals are Erlang distributed. When the claim amount is distributed as a combination of exponentials, explicit formulas for the GerberShiu expected discounted penalty function (Gerber and Shiu (1998)) and the expected total discounted cost of capital injections before ruin are obtained. The derivations rely on a resolvent density associated with an Erlang random variable, which is shown to admit an explicit. Numerical examples are provided, including an application to minimize the ruin probability via a reinsurance that makes the capital injections. This is joint work with Hailiang Yang and Zhimin Zhang.

 