Martingale ισοδύναμα μέτρα πιθανότητας και το πρόβλημα της αποτίμησης ασφαλιστικών παραγώγων CAT
Martingale equivalent probability measures and the problem of pricing CAT derivatives
SubjectΠιθανότητες ; Στοχαστικές διαδικασίες ; Διαχείριση κινδύνου -- Στατιστικές μέθοδοι ; Martingales (Mathematics) ; Probabilities ; Stochastic processes ; Risk management -- Statistical methods
In this thesis, we focus on the pricing of insurance futures for catastrophic events (CAT futures), whose underlying delivery is a Loss Index (or Loss Ratio) of Insurance service Office (ISO). Given a probability space and a stochastic process of the value of a CAT future, the existence and the uniqueness of an equivalent martingale measure, is important. In some special cases, the uniqueness of such a measure is equivalent to the completeness of securities markets and capable of solving the pricing problem. Although, as soon as we move to compound processes based on homogeneous, mixed, or doubly stochastic Poisson processes, even when completeness is present, we may lose the uniqueness of the equivalent martingale property and therefore the unique pricing property. Hence, as a first step we study the pricing of CAT futures in the context of utility maximization from the point of view of an individual agent. As a second step we study the pricing through the general equilibrium approach, where all investors maximize their utility (exchanging risks) at the same time.