A Unified Characterization of 𝑞-Optimal and Minimal Entropy Martingale Measures by Semimartingale Backward Equations

Abstract

Abstract We give a unified characterization of 𝑞-optimal martingale measures for 𝑞 ∈ [0, ∞) in an incomplete market model, where the dynamics of asset prices are described by a continuous semimartingale. According to this characterization the variance-optimal, the minimal entropy and the minimal martingale measures appear as the special cases 𝑞 = 2, 𝑞 = 1 and 𝑞 = 0 respectively. Under assumption that the Reverse Hölder condition is satisfied, the continuity (in 𝐿 1 and in entropy) of densities of 𝑞-optimal martingale measures with respect to 𝑞 is proved.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 23 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.