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We consider a general class of continuous asset price models where the drift and the volatility functions, as well as the driving Brownian motions, change at a random time $\tau$. Under minimal assumptions on the random time and on the driving Brownian motions, we study the behavior of the model in all the filtrations which naturally arise in this setting, establishing martingale representation results and characterizing the validity of the NA1 and NFLVR no-arbitrage conditions., Comment: 21 pages

The present research is motivated by the recent results of Jeanblanc and Song (2011) [10] , [11] . Our aim is to demonstrate, with the help of multiplicative systems introduced in Meyer (1979) [21] , that for any given positive F -submartingale F such that F ∞ = 1 , there exists a random time τ on some extension of the filtered probability space such that the Azema submartingale associated with τ coincides with F . Pertinent properties of this construction are studied and it is subsequently extended to the case of several correlated random times with the predetermined univariate conditional distributions.

A simple representation of the expectation of a renewal process mean with random time is obtained which leads to a renewal theoretic interpretation of certain premium calculation principles.

A generalisation of the notion of stopping time is stated, and related to similar generalisations introduced by Bahadur, Kemperman, Siegmund and others with a view to permitting auxilliary experimentation to enter into the definition of stopping rule. The main aim of this note is to draw attention to the conditional independence implicit in the definitions of these writers, and briefly indicate some consequences of this.