A minimality property of the minimal martingale measure

✍ Scribed by Martin Schweizer

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 82 KB
• Volume: 42
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(98)00180-1

✦ Synopsis

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.