Minimal Hellinger martingale measures of order \(q\)
The authors present an extension of the notion of the minimal Hellinger martingale measure (MHM) to any order \(q\neq 1\) and to the general semimartingale framework. Such an extension enables a unified formulation for many optimal martingale measures, including the minimal martingale measure of Föllmer and Schweizer, MHM of Grandits, minimal distance martingale measure of Kallsen. Under some mild conditions of integrability and the absence of arbitrage, the existence of MHM of order \(q\) is proved and described explicitly in terms of pointwise equations in \(\mathbb R^d\). The relation between the MHM concept and the utility maximization problem is treated. Particularly, applications to the maximization of the expected power utility at stopping times are given. More precisely, the authors investigate whether an agent can maximize its expected utility from terminal wealth indifferently to the liquidation time of assets (which is the market's exit time, supposed to be a stopping time). Some other frequently used market models and cases are also discussed. Applications of maximization of expected power utility with random horizon are presented.
scientific article; zbMATH DE number 5520644