On the semimartingale property via bounded logarithmic utility

Abstract

This paper provides a new version of the condition of Di Nunno et al. (2003); Di Nunno, G., Meyer-Brandis, T., Øksendal, B., Proske, F.: Optimal portfolio for an insider in a market driven by Levy processes. Quant. Financ. 6, 83–94 (2006). Ankirchner and Imkeller Annales de l’Institut Henri Poincaré (B) Probabilités et statistiques 41, 479–503 (2005) and Biagini and Øksendal Appl. Math. Optim. 52, 167–181 (2005) which ensures the semimartingale property for a large class of continuous stochastic processes. Unlike our predecessors, we base our modeling framework on the concept of portfolio proportions. This yields a short self-contained proof of the main theorem, as well as a counter example which shows that analogues of our results do not hold in the discontinuous setting.