Uniform integrability of a single jump local martingale with state-dependent characteristics

Local martingales that are not uniformly integrable martingales have recently gained attention in the stochastic processes and mathematical finance literature, being linked to special cases in arbitrage theory and the... [ view full abstract ]

Local martingales that are not uniformly integrable martingales have recently gained attention in the stochastic processes and mathematical finance literature, being linked to special cases in arbitrage theory and the occurrence of bubbles.  

We present a deterministic criterion to determine whether a single jump local martingale is a uniformly integrable martingale. Our processes are based on general, possibly explosive diffusions and a state-dependent jump hazard rate, extending results on both pure homogeneous diffusions and deterministic hazard rates. We provide natural examples of local martingales that are not uniformly integrable martingales and live on a stochastically unbounded (yet finite) time window.