Optimal Stopping and Applications

Risk Minimization in Optimal Stopping Problem and Applications

We consider an optimal stopping problem with a discrete time stochastic process where a criterion is a threshold probability. We first obtain the fundamental characterization of an optimal value and an optimal stopping time as the result of the classical optimal stopping problem, but the optimal value and the optimal stopping time depend upon a threshold value. We also give the properties of th...

Optimal Stopping and Applications Example 2: American options

Finite Horizon Optimal Stopping of Time-Discontinuous Functionals with Applications to Impulse Control with Delay

We study finite horizon optimal stopping problems for continuous time Feller-Markov processes. The functional depends on time, state and external parameters, and may exhibit discontinuities with respect to the time-variable. Both left and right-hand discontinuities are considered. We investigate the dependence of the value function on the parameters, initial state of the process and on the stop...

A Forward Algorithm for Solving Optimal Stopping Problems

We consider the optimal stopping problem for g(Zn), where Zn, n = 1, 2, . . . , is a homogeneous Markov sequence. An algorithm, called forward improvement iteration, is presented by which an optimal stopping time can be computed. Using an iterative step, this algorithm computes a sequence B0 ⊇ B1 ⊇ B2 ⊇ · · · of subsets of the state space such that the first entrance time into the intersection ...

Moment-based minimax stopping functions for sequences of random variables

Minimax-optimal stopping times and minimax (worst-case) distributions are found for the problem of stopping a sequence of uniformly bounded independent random variables, when only the means and! or variances are known, in contrast to the classical setting where the complete joint distributions of the random variables are known. Results are obtained for both the independent and i.i.d. cases, wit...