The American put is one of the oldest problems in mathematical finance. We review the development of the relevant literature over the last 40 years. Today the mainstream computational problems have been solved satisfactorily and the target of research is shifting towards the development of...

We propose a class of new robust GMM tests for endogenous structural breaks. The tests are based on supremum and average statistics derived from robust GMM estimators with a bounded influence function. They imply a bounded linearized asymptotic bias of size and power under local model...

We propose a new class of test statistics inducing accurate dual likelihood ratio tests of parametric constraints in overidentified moment conditions models. These statistics are derived from the dual likelihood implied by the exponent in the saddlepoint approximation of a general GMM estimator...

The main tools and cocepts of financial and actuarial theory are designed to handle standards, or even small risk. The aim of this paper is to reconsider some selected financial problems, in a setup including infrequent extreme risks. We first consider investors maximizing the expected utility...

In discrete time, every time-consistent dynamic monetary risk measure can be written as a composition of one-step risk measures. We exploit this structure to give new dual representation results for time-consistent convex monetary risk measures in terms of one-step penalty functions. We first...

We consider a class of law-invariant convex risk measures which have a.robust representation of the form ρ(X ) = ...... . The supremum is taken over the set of all Radon Nikodym derivatives corresponding to the set of all probability measures on B(0,1] which are absolutely continuous with...

A new class of risk measures called cash sub-additive risk measures is introduced to assess the risk of future financial, non-financial and insurance positions. The debated cash additive axiom is relaxed into the cash sub-additive axiom to preserve the original difference between the numeraire...

In this paper, we show that coherent upper and lower previsions as well as coherent risk measures are only meaningful under the assumption that one starts with initial wealth being constantly 0. This implies at least for coherent upper and lower previsions a correction of their interpretation,...

A class of contribution values for pairs of random variables is introduced as a technical tool for the problem how the risk capital needed for a portfolio of random activities should be allocated to its components. The well known allocation model with expected shortfall as corresponding risk...

It is common practice to describe the future evolution of a financial profit by a continuous-time stochastic model. A risk measure can then be viewed as a functional on a space of continuous-time stochastic processes. We extend the notions of coherent and convex risk measures to the space of...