The notion of No Free Lunch with Vanishing Risk (or NFLVR in short) w.r.t. admissible strategies depends on the choice of numeraire. Yan(1998) introduced the notion of allowable strategy and showed that condition of NFLVR w.r.t. allowable strategies is independent of the choice of numeraire and is equivalent to the existence of an equivalent martingale measure for the deflated price process. In...

We find a Stroock formula in the setting of generalized chaos expansion introduced by Nualart and Schoutens for a certain class of Lévy processes, using aMalliavin-type derivative based on the chaotic approach. As applications, we get the chaotic decomposition of the local time of a simple Lévy process as well as the chaotic expansion of the price of a financial asset and of the price of a Euro...

In this paper we review the hedging of interest rate derivatives priced under a risk-neutral measure, and we compute self-financing hedging strategies for various derivatives using the Clark-Ocone formula.

In a discrete-time financial market setting, the paper relates various concepts introduced for dynamic portfolios (both in discrete and in continuous time). These concepts are: value preserving portfolios, numeraire portfolios, interest oriented portfolios, and growth optimal portfolios. It will turn out that these concepts are all associated with a unique martingale measure which agrees with t...

In this paper we establish a one-to-one correspondence between lawinvariant convex risk measures on L∞ and L. This proves that the canonical model space for the predominant class of law-invariant convex risk measures is L.

In this paper we provide a rigorous toolkit for extending convex risk measures from L∞ to L, for p ≥ 1. Our main result is a one-to-one correspondence between law-invariant convex risk measures on L∞ and L. This proves that the canonical model space for the predominant class of law-invariant convex risk measures is L. Some significant counterexamples illustrate the many pitfalls with convex ris...

• So far we have maintained the assumption of iid data in the estimation of distributions and risk measures. However, this assumption does not hold for financial data, which are known to be intertemporally dependent, especially in the volatility. Estimation of risk measures under the assumption of iid can be viewed as unconditional estimates. In contrast, we can model the intertemporal dependen...

Abstract: Kusuoka representations provide an important and useful characterization of law invariant coherent risk measures in atomless probability spaces. However, the applicability of these results is limited by the fact that such representations do not always exist in probability spaces with atoms, such as finite probability spaces. We introduce the class of functionally coherent risk measure...

This paper analyzes four kinds of Cantonese polar questions, HO2, ME1, AA4 and A-NOTA questions in the framework of radical inquisitive semantics (Groenendijk & Roelofsen, 2010; Aher, 2012; Sano, 2014). HO2, ME1 and A-NOT-A questions have multidimensional semantics. In addition to their primary speech act of questioning, HO2 and ME1 interrogatives encode secondary assertive acts of positive and...

This paper introduces a set of axioms that define convex risk measures. Duality theory provides the representation theorem for these measures and the link with pricing rules. 2002 Published by Elsevier Science B.V. JEL classification: G11; G12; G13