We study a backward stochastic differential equation (BSDE) whose terminal condition is an integrable function of a local martingale and generator has bounded growth in z. When the local martingale is a strict local martingale, the BSDE admits at least two different solutions. Other than a...

The numéraire portfolio in a financial market is the unique positive wealth process that makes all other nonnegative wealth processes, when deflated by it, supermartingales. The numéraire portfolio depends on market characteristics, which include: (a) the information flow available to...

A financial market model where agents trade using realistic combinations of simple (i.e., finite combinations of buy-and-hold) no-short-sales strategies is considered. Minimal assumptions are made on the discounted asset-price process â in particular, the semimartingale property is not assumed....

We present a short and self-contained proof of the following result: a random time is an honest time that avoids all stopping times if and only if it coincides with the (last) time of maximum of a nonnegative local martingale with zero terminal value and no jumps while at its running supremum,...

In this paper, we analyze a real-valued reflected backward stochastic differential equation (RBSDE) with an unbounded obstacle and an unbounded terminal condition when its generator f has quadratic growth in the z-variable. In particular, we obtain existence, uniqueness, and stability results,...

We investigate the continuity of expected exponential utility maximization with respect to perturbation of the Sharpe ratio of markets. By focusing only on continuity, we impose weaker regularity conditions than those found in the literature. Specifically, we require, in addition to the...

We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards. Our development is presented in two parts. In the first part, we will develop the...

We study finite horizon optimal switching problems for hidden Markov chain models with point process observations. The controller possesses a finite range of strategies and attempts to track the state of the unobserved state variable using Bayesian updates over the discrete observations. Such a...

In this paper, we accomplish two objectives: First, we provide a new mathematical characterization of the value function for impulse control problems with implementation delay and present a direct solution method that differs from its counterparts that use quasi-variational inequalities. Our...

A change in the arrival rate of a Poisson process sometimes necessitates immediate action. If the change time is unobservable, then the design of online change detection procedures becomes important and is known as the Poisson disorder problem. Formulated and partially solved by Davis [Banach...