Μελέτη στοχαστικών διαδικασιών με υπό συνθήκη στάσιμες και ανεξάρτητες προσαυξήσεις και εφαρμογές στα χρηματοοικονομικά
Processes with conditionally stationary independent increments and applications in finance
Μπότση, Αουρόρα Λ.
SubjectΔιαχείριση κινδύνου -- Στατιστικές μέθοδοι ; Poisson processes ; Θεωρία πιθανοτήτων ; Στοχαστικές ανελίξεις -- Μαθηματικά υποδείγματα
Some basic properties and some characterizations of stochastic processes with conditionally stationary and conditionally independent increments are studied. Such processes are generalization of stochastic processes with stationary and independent increments, and have interesting applications in Risk Theory, Statistics and Finance. First, the known result that, each mixed Poisson process is a Markov process and has the polynomial property, is presented. This raises the question whether a Markov process is mixed Poisson one. Then the following problem is investigated: ”For given compound mixed Poisson process S under a probability measure P, characterize all those probability measures which are progressively equivalent to the probability measure P, and under which the distribution of S remains unchanged.” This is solved by D. Lymberopoulos and here we investigate a particular case of this problem. Finally some special cases of the above result, his relationship with the premium calculation principles and its role in the pricing of insurance derivatives are examined.