A Markov process is registered. At random moment θ the distribution of observed sequence changes. Using probability maximizing approach the optimal stopping rule for detecting the change is identified. Some explicit solution is obtained.

We show that the optimal stopping boundary for the Russian option with finite horizon can be characterized as the unique solution of a nonlinear integral equation arising from the early exercise premiumrepresentation (an explicit formula for the arbitrage-free price in terms of the optimal stopping boundary having a clear economic interpretation). The results obtained stand in a complete parall...

We consider the setting of estimating the mean of a random variable by a sequential stopping rule Monte Carlo (MC) method. The performance of a typical second moment based sequential stopping rule MC method is shown to be unreliable in such settings both by numerical examples and through analysis. By analysis and approximations, we construct a higher moment based stopping rule which is shown in...

We consider the optimal stopping of independent, discrete time sequences X1, . . . , Xn where m stops are allowed. The payoff is the sum of the stopped values. Under the assumption of convergence of related imbedded point processes to a Poisson process in the plane we derive approximatively optimal stopping times and stopping values. The solutions are obtained via a system of m differential equ...

We deal with the pricing of callable Russian options. A callable Russian option is a contract in which both of the seller and the buyer have the rights to cancel and to exercise at any time, respectively. The pricing of such an option can be formulated as an optimal stopping problem between the seller and the buyer, and is analyzed as Dynkin game. We derive the value function of callable Russia...

where S = (St)t 0 is the maximum process associated with the one-dimensional time-homogeneous diffusion X = (Xt)t 0 , the function x 7! c(x) is positive and continuous, and the supremum is taken over all stopping times of X for which the integral has finite expectation. It is proved, under no extra conditions, that this problem has a solution, i.e. the payoff is finite and there is an optimal s...

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...

We study several optimal stopping problems in which the gains process is a Brownian bridge or a functional of a Brownian bridge. Our examples constitute natural finitehorizon optimal stopping problems with explicit solutions.

When prospect theory (PT) is applied in a dynamic context, the probability weighting component brings new challenges. We study PT agents facing optimal timing decisions and consider the impact of allowing them to follow randomized strategies. In a continuous-time model of gambling and optimal stopping, Ebert and Strack (2015) show that a naive PT investor with access only to pure strategies nev...

This paper introduces a new employee option plan for lowand mid-level employees. The option plan is a possibility for the employee to exercise an accrual account at any time before maturity contingent on the stock price being above a strike level. The option is American in nature and is a combination of an accrual account and a digital option with a strike price. The optimal stopping problem as...