The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any...

In this article we consider a game theoretic approach to the Risk-Sensitive Benchmarked Asset Management problem (RSBAM) of Davis and Lleo \cite{DL}. In particular, we consider a stochastic differential game between two players, namely, the investor who has a power utility while the second...

The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any...

We consider the problem of a trustee faced with investing a sum of money, the interest from which will be received by one party (the life-tenant) during his lifetime while the capital will go to another party (the survivor) on the death of the life-tenant. We assume mat there are "n"+ 1 assets...

We establish necessary and sufficient conditions for an H-martingale to be representable with respect to a collection, of local martingales. "M" H("P") is representable if and only if "M" is a local martingale under all p.m.'s "Q" which are "uniformly equivalent" to "P" and which make all the...

We show that the problem of pricing the American put is equivalent to solving an optimal stopping problem. the optimal stopping problem gives rise to a parabolic free-boundary problem. We show there is a unique solution to this problem which has a lower boundary. We identify an integral equation...

We discuss three forms of convergence in distribution which are stronger than the normal weak convergence, and are non-topological in nature. We give Storokhod representation results for two of these modes of convergence, and give applications to sufficient statistics and conditioned Markov...

An embedding of an arbitrary centred law [mu] in a Brownian motion (that is a stopping time T and a Brownian motion B such that (Bt)=[mu] and (Bt[Lambda]T; t[greater-or-equal, slanted]0) is found such that B*T has a law which dominates that of M*[tau], where the pair (M, [tau]) is any other ui...