Conditional coherent risk measures and regime-switching conic pricing

This paper introduces and represents conditional coherent risk measures as essential suprema of conditional expectations over a convex set of probability measures and as distorted expectations given a concave distortion function. A model is then developed for the bid and ask prices of a European-type asset by a conic formulation. The price process is governed by a modified geometric Brownian motion whose drift and diffusion coefficients depend on a Markov chain. The bid and ask prices of a European-type asset are then characterized using conic quantization.