VALUATIONS AND DYNAMIC CONVEX RISK MEASURES

Valuations and dynamic convex risk measures

This paper approaches the definition and properties of dynamic convex risk measures through the notion of a family of concave valuation operators satisfying certain simple and credible axioms. Exploring these in the simplest context of a finite time set and finite sample space, we find natural risk-transfer and time-consistency properties for a firm seeking to spread its risk across a group of ...

Conditional and dynamic convex risk measures

We extend the definition of a convex risk measure to a conditional framework where additional information is available. We characterize these risk measures through the associated acceptance sets and prove a representation result in terms of conditional expectations. As an example we consider the class of conditional entropic risk measures. A new regularity property of conditional risk measures ...

Optimal Stopping for Dynamic Convex Risk Measures

We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem in which the decision maker uses a dynamic convex risk measure to evaluate future rewards.

Dynamic convex risk measures: time consistency, prudence, and sustainability

Convex and coherent risk measures

We discuss the quantification of financial risk in terms of monetary risk measures. Special emphasis is on dual representations of convex risk measures, relations to expected utility and other valuation concepts, conditioning, and consistency in discrete time.