The Optimal Stopping Problem of Dupuis and Wang: A Generalization

In this paper, we study the optimal stopping problem of Dupuis and Wang analyzed in [7]. In this problem, the underlying follows a linear diffusion but the decision maker is not allowed to stop at any time she desires but rather on the jump times of an independent Poisson process. In [7], the authors solve this problem in the case where the underlying is a geometric Brownian motion and the payoff function is of American call option type. In the current study, we will this problem under weak assumptions on both the underlying and the payoff. We also demonstrate that the results of [7] are recovered from ours.Optimal stopping, linear diffusion, free boundary problem, Poisson process

On Infinite Horizon Optimal Stopping of General Random Walk

The objective of this study is to provide an alternative characterization of the optimal value function of a certain Black- Scholes-type optimal stopping problem where the underlying stochastic process is a general random walk, i.e. the process constituted by partial sums of an IID sequence of random variables. Furthermore, the pasting principle of this optimal stopping problem is studied.General random walk, optimal stopping, minimal functions, continuous pasting

Bounded variation control of Itô diffusions with exogenously restricted intervention times

In this paper, bounded variation control of one-dimensional diffusion processes is considered. We assume that the agent is allowed to control the diffusion only at the jump times of an observable, independent Poisson process. The agent's objective is to maximize the expected present value of the cumulative payoff generated by the controlled diffusion over its lifetime. We propose a relatively weak set of assumptions on the underlying diffusion and the instantaneous payoff structure, under which we solve the problem in closed form. Moreover, we illustrate the main results with an explicit example

Do Standard Real Option Models Overestimate the Required Rate of Return of Real Estate Investment Opportunities?

We consider how the inter-temporal discreteness of the revenue and cost processes affect the optimal timing of a real estate investment opportunity in comparison with the investment timing strategy obtained by relying on the traditional continuous real option model. We characterize both optimal investment rules explicitly and show that the continuous model may lead to a significantly higher required rate of return than the discrete model. Hence, our results show that the use of continuous time models leads to smaller and suboptimal amount of investment. Our numerical illustrations also indicate that this difference grows as volatility increases. Consequently, even though higher volatility decelerates investment in the discrete case as well, it decelerates it less than the continuous model would predict.Real options, real estate investment timing, exchange option

Some results on optimal stopping under phase-type distributed implementation delay

We study optimal stopping of strong Markov processes under random implementation delay. By random implementation delay we mean the following: the payoff is not realised immediately when the process is stopped but rather after a random waiting period. The distribution of the random waiting period is assumed to be phase-type. We prove first a general result on the solvability of the problem. Then we study the case of Coxian distribution both in general and with scalar diffusion dynamics in more detail. The study is concluded with two explicit examples