Stochastic dominance (SD) is a very useful tool in various areas of economics and finance. the purpose of this paper is to provide the results of SD relations developed in other areas such as applied probability which, we believe, are useful for many portfolio selection problems. In particular,...

In recent years, it has become common to use a Markov chain model to describe the dynamics of a firm's credit rating as an indicator of the likelihood of default. Such a model can be used not only for describing the dynamics but also for valuing risky discount bonds. The aim of this paper is to...

The Black-Scholes option price is increasing and convex with respect to the initial stock price. increasing with respect to volatility and instantaneous interest rate, and decreasing and convex with respect to the strike price. These results have been extended in various directions. In...