q-fin updates on arXiv.org
Tue, 11 Feb 2020 06:01:33 GMT language
In a general one-sided limit order book where the unaffected price process
follows a Levy process, we consider the problem for an investor with constant
absolute risk aversion to optimally liquidate a given large position of shares.
Since liquidation normally takes place within a short period of time, modelling
the risk as a Levy process should provide a realistic model with good
statistical fit to observed market data, thus providing a realistic reflection
of the investors market risk. We can reduce the optimisation problem to a
deterministic two-dimensional singular problem, to which we are able to derive
an explicit solution in terms of the model data. In particular we find an
expression for the optimal intervention boundary, which completely characterise
the optimal liquidation strategy.