Feasible statistical modelling for extremes in ecology and finance
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The project will pursue the following aims:
Theoretical study of different modifications of the score function in order to obtain consistent, robust and possibly efficient estimators of extreme values. In particular we aim to construct estimators well applicable for ecological and financial areas.
Theoretical study of multivariate of compounds with equal number of summands and estimation of its parameters in some particular cases.
Applications to finance. Different types of claims has different sizes, therefore it is better to model them separately. Multivariate compounds with equal number of summands are appropriate for modelling the distribution of the number of customers of fixed types, that arrive in an insurance company up to time t. Therefore they are useful e.g. for modelling of the risk reserve process, the total claim amount up to time t and for estimating of probability of ruin.
Theoretical study of alternatives of ARCH/GARCH models with heavy tailed innovations.
Applications to ecology. In particularly to snow extremes, methane emissions and water quality.