Jocelyne Bion-Nadal

Dynamic risk measures: Time consistency and risk measures from BMO martingales

Abstract Time consistency is a crucial property for dynamic risk measures. Making use of the dual representation for conditional risk measures, we characterize the time consistency by a cocycle condition for the minimal penalty function. Taking advantage of this cocycle condition, we introduce a new methodology for the construction of time-consistent dynamic risk measures. Starting with BMO martingales, we provide new classes of time-consistent dynamic risk measures. These families generalize those obtained from backward stochastic differential equations. Quite importantly, starting with right-continuous BMO martingales, this construction naturally leads to paths with jumps.

Risk measuring under model uncertainty

The framework of this paper is that of risk measuring under uncertainty, which is when no reference probability measure is given. To every regular convex risk measure on

Dynamic quasi-concave performance measures

{\cal C}_b(\Omega)

Dynamic no-good-deal pricing measures and extension theorems for linear operators on L∞

, we associate a unique equivalence class of probability measures on Borel sets, characterizing the riskless non positive elements of

Dynamic Risk Measures and Path-Dependent Second Order PDEs

{\cal C}_b(\Omega)

Time consistent dynamic risk processes

. We prove that the convex risk measure has a dual representation with a countable set of probability measures absolutely continuous with respect to a certain probability measure in this class. To get these results we study the topological properties of the dual of the Banach space

Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk

L^1(c)

Dynamic risk measuring under model uncertainty: taking advantage of the hidden probability measure

associated to a capacity

Time consistent convex Feller processes and non linear second order partial differential equations

c

Time Consistent Dynamic Limit Order Books Calibrated on Options

. As application we obtain that every