We present an arbitrage free theoretical framework for modeling bid and ask prices of
dividend paying securities in a discrete time setup using the theory of dynamic acceptability
indices. In the first part of the paper we develop the theory of dynamic subscale invariant
performance measures, on a general filtered probability space. We prove a representation
theorem for such measures in terms of a family of dynamic convex risk measures, and we
provide a representation of dynamic risk measures in terms of g-expectations, and solutions …

… Specifically, we have advanced dynamic aspects of conic finance by developing an arbitrage
free theoretical framework for modeling bid and ask prices of dividend paying securities using
the theory of dynamic acceptability indices. This has been done within the framework of general
probability spaces and discrete time. In the … In particular, we contribute here to the so called
dynamic conic finance theory. In the second part – Chapter 3 – motivated by the applications
to the problem of adaptive robust hedging, we develop a methodology for recursive …