Utility maximization under risk constraints and incomplete information for a market with a change point. Issue 5 (3rd September 2017)

• Record Type: Journal Article
• Authors: Janke, Oliver
• Is Part Of: Applied mathematical finance. Volume 24:Issue 5(2017)
• Page Start: 451
• Page End: 484
• Publication Date: 2017-09-03
• Subjects: Utility maximization -- risk constraint -- incomplete information -- change point -- enlargement of filtrations; Business mathematics -- Periodicals; 650.0151
• DOI: 10.1080/1350486X.2017.1409080
• Languages: English
• ISSNs: 1350-486X

Abstract

ABSTRACT: In this article, we consider an optimization problem of expected utility maximization of continuous-time trading in a financial market. This trading is constrained by a benchmark for a utility-based shortfall risk measure. The market consists of one asset whose price process is modelled by a Geometric Brownian motion where the market parameters change at a random time. The information flow is modelled by initially and progressively enlarged filtrations which represent the knowledge about the price process, the Brownian motion and the random time. We solve the maximization problem and give the optimal terminal wealth depending on these different filtrations for general utility functions by using martingale representation results for the corresponding filtration.