Optimal Stopping and Applications Example 2: American options

Optimal stopping and American options with discrete dividends and exogenous risk

In this paper we analyze some problems arising in the evaluation of American options when the underlying security pays discrete dividends. To this aim, we study the problem of maximizing the expected gain process over stopping times taking values in the union of disjoint, real compact sets. The results we obtain can be applied to evaluate options with restrictions on exercise periods, but are a...

Optimal stopping for a diffusion with jumps

In this paper we give the closed form solution of some optimal stopping problems for processes derived from a diffusion with jumps. Within the possible applications, the results can be interpreted as pricing perpetual American Options under diffusion-jump information.

Characterization of Optimal Stopping Regions of American Asian and Lookback Options

A general framework is developed to analyze the optimal stopping (exercise) regions of American path dependent options with either Asian feature or lookback feature. We examine the monotonicity properties of the option values and stopping regions with respect to the interest rate, dividend yield and time. From the ordering properties of the values of American lookback options and American Asian...

A Note on Optimal Stopping in Models with Delay

It is known that optimal stopping problems form an important class of optimal control problems having applications in stochastic calculus (maximal inequalities), statistics (sequential analysis) and mathematical finance (American options). The results about the relationship between optimal stopping problems for Markov processes and free-boundary problems for partial differential equations often...

Optimal stopping and American options