We consider a new approach towards stochastic dominance rules which allows measuring the degree of domination or violation of a given stochastic order and represents a way of describing stochastic orders in general. Examples are provided for the n-th order stochastic dominance and stochastic...

This paper examines the pricing of barrier options when the price of the underlying asset is modeled by a branching process in a random environment (BPRE). We derive an analytical formula for the price of an up-and-out call option, one form of a barrier option. Calibration of the model...