This paper provides the mathematical foundation for polynomial diffusions. They play an important role in a growing range of applications in finance, including financial market models for interest rates, credit risk, stochastic volatility, commodities and electricity. Uniqueness of polynomial...

Diffusion of new products is an important problem in marketing research. One of the most prominent models in diffusion theory is the Bass Diffusion model that describes the number of adopters of new products as a differential equation. More recently, diffusion of products has been studied using...

Forecasting the diffusion of innovations plays a major role in managing technology development and in engineering management overall. In this paper, we extend the conventional Bass model stochastically by specifying the error process of sales as log-normal and mean-reverting. Our model satisfies...

In this paper we study the stochastic area swept by a regular time-homogeneous diffusion till a stopping time. This unifies some recent literature in this area. Through stochastic time change we establish a link between the stochastic area and the stopping time of another associated...

Korean Abstract : 이 논문에서는 한국의 주별 익일물 콜금리를 사용해 국면전환 확산과정모형을 추정했다. 일반적인 비선형 추세 함수와 분산 탄력성이 상수인 변동성 함수를 갖는 확산과정모형에서 모수들이 경제상황에 따라...

Using the path-integral formalism we develop an accurate and easy-to-compute semi-analytical approximation to transition probabilities and Arrow-Debreu densities for arbitrary diffusions. We illustrate the accuracy of the method by presenting results for the Black-Karasinski model for which the...