We apply a new simulation scheme proposed by Kusuoka to finance problems. By using this method, we achieve 6500 times faster simulation than traditional Euler–Maruyama scheme.

The master equation for the reversible reaction A+A⇌0 is considered in Poisson representation, where it is equivalent to a Langevin equation with imaginary noise for a complex stochastic variable φ. Such Langevin equations appear quite generally in field-theoretic treatments of...

In this paper, we develop approximations that yield insight into the joint optimization of capacity and inventory,and how the optimal inventory policy varies with capacity investment in a single-product, single-station, make-to-stock manufacturing system in which inventory is managed through a...

Much of the work on path-dependent options assumes that the underlying asset price follows geometric Brownian motion with constant volatility. This paper uses a more general assumption for the asset price process that provides a better fit to the empirical observations. We use the so-called...

An analytical study of the evolution of the distribution of firm size in an industry is presented. A drift-diffusion model is proposed to express the time-evolution of density of firm size within the industry. The model blends the conventional, more or less static, determinants with the kinds of...

WE consider a particular type of randomly observed continuous time process, in accordance with the characteristics of dataset coming from financial markets. We adapt the concept of Local Time by defining from the discrete observations an Empirical Local Time and we prove it converges under...