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Stochastic Monotonicity and Duality of<i>k</i>th Order with Application to Put-Call Symmetry of Powered Options
We introduce a notion of $k$th order stochastic monotonicity and duality that allows one to unify the notion used in insurance mathematics (sometimes refereed to as Siegmund's duality) for the study of ruin probability and the duality responsible for the so-called put - call symmetries in option pricing. Our general …