We consider a long-term average profit–maximizing admission control problem in an M/M/1
queuing system with unknown service and arrival rates. With a fixed reward collected upon …

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 consider a diffusive model for optimally distributing dividends, while allowing for
Knightian model ambiguity concerning the drift of the surplus process. We show that the …

We propose a model uncertainty approach to heavy traffic asymptotics that allows for a high
level of uncertainty. That is, the uncertainty classes of underlying distributions accommodate …

We consider a general class of singular control problems with state constraints. Budhiraja
and Ross [Ann. Appl. Probab., 16 (2006), pp. 2235--2255] established the existence of …

We consider a multidimentional Brownian control problem (BCP) with model uncertainty that
formally emerges from a multiclass M/M/1 queueing control problem under heavy traffic with …

We consider admission control for a first-in first-out single class single server queueing
model with Poisson arrivals and exponential service times. Specifically, there is a dispatcher …

We consider a critically-loaded multiclass queueing control problem with model uncertainty.
The model consists of I types of customers and a single server. At any time instant, a …

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 …

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