We will generalize the Black-Scholes option pricing formula by incorporating stochastic interest rates. Although the existing literature has obtained some formulae for stock options under stochastic interest rates, the closed-form solutions have been known only under the Gaussian (Merton type)...

We illustrate how to use the X-12-ARIMA program developed by the U. S. Census Bureau when you have to make seasonal adjustment data at the statistical division of the central government. As an illustration we use the Hojinkigyo-Toukei, which is one of the major statistics including sales and...

Recently the various types of the equity-linked insurance have been introduced and actively traded in Japanese insurance markets. We investigate the basic problems of the actuarial risk management methods for those products based on the Markovian regime-switching time series model, which was...

Asymptotic expansions are made for the distributions of the Maximum Empirical Likelihood (MEL) estimator and the Estimating Equation (EE) estimator (or the Generalized Method of Moments (GMM) in econometrics) for the coefficients of a single structural equation in a system of linear simultaneous...

Kunitomo and Takahashi (1995), and Takahashi (1997) have proposed a new methodology, called Small Disturbance Asymptotics, for the valuation problem of financial contingent claims when the underlying asset prices follow a general class of continuous Ito processes. It can be applicable to a wide...