We connect singular control problems arising in irreversible investment to obstacle problems for second-order PDEs and characterise the free boundary.
Optimal consumption-investment policies are derived for an investor with Epstein-Zin recursive preferences under incomplete markets.
We analyse Nash equilibria in large-population stochastic differential games where agents interact through a common noise term.
The Almgren-Chriss framework is extended to account for stochastic liquidity, and the resulting singular control problem is solved via dynamic programming.
We study the Hamilton-Jacobi-Bellman equation arising in stochastic optimal control problems with controlled diffusion. Existence and uniqueness of viscosity solutions are established under standard regularity assumptions.