Deux applications de la décomposition de Galtchouk-Kunita-Watanabe

Abstract

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Local Risk-Minimization for Defaultable Claims with Recovery Process

“…2, Theorem 1 of [25] guarantees that (SC) is automatically satisfied. For more general results in this direction, see [11]. Additional results on the relation between (SC) and properties of absence of arbitrage for the process X can be found in [12].…”

Drift operator in a viable expansion of information flow

“…Its name "raw structure condition" is inspired from the literature. In [11,38], a condition called "structure condition" has been introduced, which has played important role in the study of incomplete market, especially of the minimal martingale measure and of the Follmer-Schweizer decomposition. The structure condition, defined for d-dimensional special semimartingales X = X 0 + M + A, has two aspects.…”

“…There exists a huge literature (cf. for example, [9,11,12,16,17,27,31,30,29,33,37,38,39,42]). Recently, there is a particular attention on the viability problem related to expansions of information flow (cf.…”

On Fefferman and Burkholder–Davis–Gundy inequalities for ℰ-martingales

“…The existence of λ as well as finiteness of K T is related to arbitrage properties as shown by Delbaen and Schachermayer (1996a). When X is a bounded process admitting a bounded equivalent martingale measure, it follows from Choulli and Stricker (1996) that X satisfies the structure condition. In the case where X is continuous, the structure condition is a necessary condition for the existence of an equivalent local martingale measure.…”

“…In the case where X is continuous, the structure condition is a necessary condition for the existence of an equivalent local martingale measure. Also in the case where X is continuous, the finiteness of K T is independent of the choice of probability measure, as shown in Delbaen and Shirakawa (1996) or Choulli and Stricker (1996). For the interpretation of K we refer to Schweizer (1994).…”