Saul D. Jacka

Doob's inequalities revisited: a maximal H1-embedding

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 embedding of [mu] in a martingale.

On strong forms of weak convergence

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 processes, which are more difficult to obtain using weak convergence.

No arbitrage and closure results for trading cones with transaction costs

AbstractIn this paper, we consider trading with proportional transaction costs as in Schachermayer’s paper (Schachermayer in Math. Finance 14:19–48, 2004). We give a necessary and sufficient condition for

Monotonicity of the value function for a two-dimensional optimal stopping problem

{\mathcal{A}}

The equivalent martingale measure conditions in a general model for interest rates

, the cone of claims attainable from zero endowment, to be closed. Then we show how to define a revised set of trading prices in such a way that, firstly, the corresponding cone of claims attainable for zero endowment,

Markov chain approximations for transition densities of Lévy processes

{\tilde{ {\mathcal{A}}}}

ON THE DENSITY OF PROPERLY MAXIMAL CLAIMS IN FINANCIAL MARKETS WITH TRANSACTION COSTS.

, does obey the fundamental theorem of asset pricing and, secondly, if

Conditioning an additive functional of a Markov chain to stay nonnegative. II. Hitting a high level

{\tilde{ {\mathcal{A}}}}

Conditioning an additive functional of a markov chain to stay nonnegative. I. Survival for a long time

is arbitrage-free then it is the closure of

Game-theoretic approach to risk-sensitive benchmarked asset management

{\mathcal{A}}