A minimality property of the minimal martingale measure

Martin Schweizer

Let X be a continuous adapted process for which there exists an equivalent local martingale measure (ELMM). The minimal martingale measure P is the unique ELMM for X with the property that local P-martingales strongly orthogonal to the P-martingale part of X are also local P-martingales. We prove that if P exists, it minimizes the reverse relative entropy H(P|Q) over all ELMMs Q for X. A counterexample shows that the assumption of continuity cannot be dropped. -- relative entropy ; minimal martingale measure ; equivalent martingale measures

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Year of publication:	1998
Authors:	Schweizer, Martin
Institutions:	Sonderforschungsbereich Quantifikation und Simulation Ökonomischer Prozesse (contributor)
Publisher:	Berlin : Humboldt-Universität
Subject:	Theorie \| Theory \| Statistische Methodenlehre \| Statistical theory \| Stochastischer Prozess \| Stochastic process \| Martingal \| Martingale