This paper extends the analytical valuation of options on the maximum or the minimum of several risky assets in several directions. The first extension consists in including more assets in the payoff and making the latter more flexible by adding knock-in and knock-out provisions. The second...

The main results imply that the probability P(Z∈A+θ) is Schur-concave/Schur-convex in (θ12,…,θk2) provided that the indicator function of a set A in Rk is so, respectively; here, θ=(θ1,…,θk)∈Rk and Z is a standard normal random vector in Rk. Moreover, it is shown that the...

In this paper, we suggest the new variable selection procedure, called MEC, for linear discriminant rule in the high dimensional and large sample setup. MEC is derived as a second-order unbiased estimator of the misclassification error probability of the linear discriminant rule (LDR). It is...