Ουδέτερες κινδύνου κατανομές πιθανότητας μεμειγμένων στοχαστικών διαδικασιών και εφαρμογές
Risk neutral probability distributions for mixed stochastic processes with applications
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Keywords
Μεικτές στοχαστικές διαδικασίες ; Μεικτές ανανεωτικές διαδικασίες ; Μεικτές διαδικασίες Poisson ; Αλλαγή μέτρου πιθανότητας ; Αρχές υπολογισμού ασφαλίστρου ; Φυσιολογικές δεσμευμένες πιθανότητεςAbstract
In this PhD thesis we prove first, under a mild assumption, that within the class of mixed renewal processes the basic question when a Markov process is a mixed Poisson one with mixing parameter a random variable is answered to the positive. The latter implies the equivalence of the Markov processes, the mixed Poisson processes and the processes that satisfy the multinomial property, within the class of mixed renewal processes. A second consequence of the latter result is the equivalence, under a mild assumption, of all known to us definitions of the mixed Poisson processes. Generalizing an earlier result of Delbaen & Haezendonck we present, for a given compound renewal process S under a probability measure P, a characterization of all probability measures Q on the domain of P, such that P and Q are progressively equivalent and S remains a compound renewal process under Q. As a consequence, it is proven that every compound renewal process can be converted into a compound Poisson one under a change of measures, and some applications to premium calculation principles are presented. The latter result is then generalized for the compound mixed renewal processes, which are of greater interest, since they are a proper model for studying inhomogeneous portfolios of insurance companies. This result has applications in pricing actuarial risks and generalizes the main result of Lyberopoulos PhD Thesis [1], Theorem 7.2.9.
Department
Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής ΕπιστήμηςNumber of pages
156Language
GreekCollections
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Attribution-NonCommercial-NoDerivatives 4.0 Διεθνές
Attribution-NonCommercial-NoDerivatives 4.0 Διεθνές