we give an approximate algorithm of computing holonomic systems of linear differential equations for definite integrals with parameters. We show that this algorithm gives a correct answer in finite steps, but we have no general stopping condition. We apply the approximate method to find differential equations for integrals associated to smooth Fano polytopes. They are interested in the study of...

We study the optimal timing of derivative purchases in incomplete markets. In our model, an investor attempts to maximize the spread between her model price and the offered market price through optimally timing her purchase. Both the investor and the market value the options by risk-neutral expectations but under different equivalent martingale measures representing different market views. The ...

We consider a class of infinite-time horizon optimal stopping problems for spectrally negative Lévy processes. Focusing on strategies of threshold type, we write explicit expressions for the corresponding expected payoff via the scale function, and further pursue optimal candidate threshold levels. We obtain and show the equivalence of the continuous/smooth fit condition and the first-order con...

Discrete choice models are commonly used in transportation planning and modeling, but their theoretical basis and their applications have been mainly developed in a static context. We propose to develop an estimation technique for analyzing the impact of technological change on the dynamics of consumer demand. The proposed research presents a dynamic model of consumer demand that explicitly acc...

Stopping accuracy is one of the most important indexes of efficiency of automatic train operation (ATO) systems. Traditional stopping control algorithms in ATO systems have some drawbacks, as many factors have not been taken into account. In the large amount of fieldcollected data about stopping accuracy there are many factors (e.g. system delays, stopping time, net pressure) which affecting st...

We consider callable Russian options with the finite maturity. Callable Russian option is a contract that the seller and the buyer have the rights to cancel and to exercise it at any time, respectively. We discuss the pricing model of callable Russian options when the stock pays dividends continuously. We show that the pricing model can be formulated as a coupled optimal stopping problem which ...

We show that the optimal stopping boundary for the early exercise Asian call option with floating strike can be characterized as the unique solution of a nonlinear integral equation arising from the early exercise premium representation (an explicit formula for the arbitrage-free price in terms of the optimal stopping boundary). The key argument in the proof relies upon a local time-space formula.

We consider a continuously observable process, which behaves like a standard Brownian motion up to a random time τ1, and as a Brownian motion with a known drift after τ1. At a stopping-time τ2 that happens after the time τ1, an observable event occurs. We address the problem of detecting the change in the system’s behaviour prior to the occurrence of the observable event. In particular, our for...

The first part of this paper summarises the essential facts on general optimal stopping theory for time-homogeneous diffusion processes in R. The results displayed are stated in a little greater generality, but in such a way that they are neither too restrictive nor too complicated. The second part presents equations for the value function and the optimal stopping boundary as a free-boundary (S...