Το κλασσικό μοντέλο της θεωρίας κινδύνου με ρευστοποιημένα αποθεματικά, επενδύσεις και μερίσματα
The classical risk model with liquid reserves, credit interest rate and threshold dividends
KeywordsΣτοχαστικές διαδικασίες ; Στοχαστικά μοντέλα ; Κλασσικό μοντέλο θεωρίας κινδύνων ; Διαχείριση κινδύνου ; Στρατηγικά μερίσματα ; Επενδύσεις ; Ρευστοποιημένα αποθεματικά ; Συνάρτηση Gerber-Shiu ; Poisson processes
The aim of this diploma thesis is to study various ruin measures as well as the type of dividend distribution paid to beneficiaries in the stochastic process that links between the intermediate times of risk exposure and the corresponding amounts of compensation required. Chapter 1 describes in detail the classic model of risk theory and presents some significant results for the Gerber-Shiu penalized penalty function for this model. An extensive description of the generalized Erlang Renewable Risk Model is given below, a special case of which is the classic model of risk theory. Chapter 2 adds the fixed dividend strategy and presents analytical results for the Gerber-Shiu function and the discounted dividend moments under this strategy for both the classic model and the generalized Erlang Renewable Model of Risk Theory. In Chapter 3 we modify the Poisson surplus model for an insurer by including liquidated stocks and surplus interest. We then study the probability of ruin and other ruin-related amounts in the modified Poisson surplus process through the Gerber-Shiu function and analyze the impact of interest and liquidity reserves on the probability of ruin, the deficit at the time of ruin and other amounts associated with ruin. Chapter 4 includes liquid reserves, interest and dividends in the Poisson surplus composite process. Thereafter, liquidity, interest rate, threshold, and dividend rate interactions will be discussed in the proposed risk model by considering the expected discounted penalty function and the expected present value of the dividends paid up to the time of the ruin. In chapter 5 we consider a ruin model where the surplus of an insurance company is built so that part of the current surplus is kept available at all times and the remaining part is invested through the Gerber-Shiu function.