English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study a constrained stochastic control problem with jumps; the jump timesof the controlled process are given by a Poisson process. The cost functionalcomprises quadratic components for an absolutely continuous control and thecontrolled process and an absolute value component for the control of the jumpsize of the process. We characterize the value function by a "polynomial" ofdegree two whose coefficients depend on the state of the system; thesecoefficients are given by a coupled system of ODEs. The problem hence reducesfrom solving the Hamilton Jacobi Bellman (HJB) equation (i.e., a PDE) tosolving an ODE whose solution is available in closed form. The state space isseparated by a time dependent boundary into a continuation region where theoptimal jump size of the controlled process is positive and a stopping regionwhere it is zero. We apply the optimization problem to a problem faced byinvestors in the financial market who have to liquidate a position in a riskyasset and have access to a dark pool with adverse selection.

An explicit solution of a non-linear quadratic constrained stochastic  control problem with an application to optimal liquidation in dark pools with  adverse selection