Lukasz Szpruch — Page 4

arXiv2011

On Markovian solutions to Markov Chain BSDEs

We study (backward) stochastic differential equations with noise coming from a finite state Markov chain. We show that, for the solutions of these equations to be `Markovian', in the sense that they are deterministic functions of the state of the underlying chain, the integrand must be of a specific form. This allows us to connect these equations to coupled systems of ODEs, and hence to give fast numerical methods for the evaluation of Markov-Chain BSDEs.

math.PR↗

arXiv2011

A limit order book model for latency arbitrage

We consider a single security market based on a limit order book and two investors, with different speeds of trade execution. If the fast investor can front-run the slower investor, we show that this allows the fast trader to obtain risk free profits, but that these profits cannot be scaled. We derive the fast trader's optimal behaviour when she has only distributional knowledge of the slow trader's actions, with few restrictions on the possible prior distributions. We also consider the slower trader's response to the presence of a fast trader in a market, and the effects of the introduction of a `Tobin tax' on financial transactions. We show that such a tax can lead to the elimination of profits from front-running strategies. Consequently, a Tobin tax can both increase market efficiency and attract traders to a market.

q-fin.TR↗