Ανάλυση διαδικασιών πλεονάσματος στη θεωρία χρεοκοπίας με τυχαία ασφάλιστρα

Χαραλαμποπούλου, Αμαλία

Surplus analysis in ruin theory with stochastic premiums

Master Thesis

Author

Χαραλαμποπούλου, Αμαλία

Date

2021-11

Abstract

The current paper generalizes the classic model of risk theory according to which premiums are not collected at a constant rate, but are described by a complex stochastic process. These surplus processes will be analyzed by considering various dependency structures between the inter-claim times and inter-premium times. For the above, results will be given through the study of the corresponding expected discounted Gerber Shiu penalty functions. In addition, the work studies and analyzes various risk measures, such as the ruin probability or the ruin time, the time to ruin theory, through the Gerber-Shiu penalty function. Chapter 1 is an introductory part that analyzes the basic concepts from ruin theory, gives a brief description of the classic model , known as the Cramér-Lundberg model, of risk theory as well as the expected discounted Gerber-Shiu penalty function and discusses the solution of the defective renewal equation for this function. Chapter 2 examines the risk model with stochastic premiums. More specifically, we will consider that premiums are not collected at a constant rate and are described by a a Poisson process. Chapter 3 examines the risk model with stochastic premiums and dependencies. Specifically, we will extend this model considering that there is a dependency between claim sizes, premiums and inter-claim times. Finally, Chapter 4 examines the model with stochastic premiums, dependencies and dividend strategies. In particular, under the threshold dividend strategy, various dependencies between claims sizes and inter-claim times in which they occur will be considered.

Postgraduate Studies Programme

Αναλογιστική Επιστήμη και Διοικητική Κινδύνου

Department

Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

Number of pages

109

Language

Greek

URI

https://dione.lib.unipi.gr/xmlui/handle/unipi/13934
http://dx.doi.org/10.26267/unipi_dione/1357

Collections

Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

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Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα