We revisit the classical theory of stochastic integral convergence on Skorokhod space,
providing a new comprehensive treatment under Skorokhod's J1 and M1 topologies based …

In this paper, we examine the stationary relaxed singular control problem within a multi-
dimensional framework for a single agent, as well as its Mean Field Game (MFG) equivalent …

We establish a probabilistic framework for analysing extended mean-field games with multi-
dimensional singular controls and state-dependent jump dynamics and costs. Two key …

We consider an ergodic harvesting problem with model ambiguity that arises from biology.
To account for the ambiguity, the problem is constructed as a stochastic game with two …

We characterize the optimal control for a class of singular stochastic control problems as the
unique solution to a related Skorokhod reflection problem. The optimization problems …

This paper establishes the existence of equilibria result of a class of mean field games with
singular controls. The interaction takes place through both states and controls. A relaxed …

This paper establishes the existence of equilibria result of a class of mean field games with
singular controls. The interaction takes place through both states and controls. A relaxed …

We revisit the classical problem of optimal payment of dividends and determine the degree
to which the diffusion approximation serves as a valid approximation of the classical risk …

We consider extended mean-field control problems with multi-dimensional singular controls.
A key challenge when analysing singular controls are jump costs. When controls are one …

Stochastic processes play a pivotal role in modeling across various domains, including
finance, biology, queueing systems, and networks. This thesis delves into several theoretical …