This note deals with the question: what remains of the Burkholder-Davis-Gundy inequalities when stopping times T are replaced by arbitrary random times [rho]? We prove that these inequalities still hold when T is a pseudo-stopping time and never holds for ends of predictable sets.

This paper demonstrates the usefulness and importance of the concept of honest times to financial modeling. It studies a financial market with asset prices that follow jump-diffusions with negative jumps. The central building block of the market model is its growth optimal portfolio (GOP), which...

This paper demonstrates the usefulness and importance of the concept of honest times to financial modeling. It studies a financial market with asset prices that follow jump-diffusions with negative jumps. The central building block of the market model is its growth optimal portfolio (GOP), which...

Given a random time, we give some characterizations of the set of martingales for which the stopping theorems still hold. We also investigate how the stopping theorems are modified when we consider arbitrary random times. To this end, we introduce some families of martingales with remarkable...

In this paper, we consider the special class of positive local submartingales (Xt) of the form Xt=Nt+At, where the measure is carried by the set {t:Xt=0}. We show that many examples of stochastic processes studied in the literature are in this class and propose a unified approach based on...

Copulas are a general tool to construct multivariate distributions and to investigate dependence structure between random variables. However, the concept of copula is not popular in Finance. In this paper, we show that copulas can be extensively used to solve many financial problems.

In this paper, for any submartingale of class (Σ) defined on a filtered probability space (Ω,F,P,(Ft)t≥0) satisfying some technical conditions, we associate a σ-finite measure Q on (Ω,F), such that for all t≥0, and for all events Λt∈Ft: Q[Λt,g≤t]=EP[1ΛtXt], where g is the last...

We use the theory of coherent measures to look at the problem of surplus sharing in an insurance business. The surplus share of an insured is calculated by the surplus premium in the contract. The theory of coherent risk measures and the resulting capital allocation gives a way to divide the...