MULTIPLICATIVE APPROXIMATION OF WEALTH PROCESSES INVOLVING NO‐SHORT‐SALES STRATEGIES VIA SIMPLE TRADING. (3rd February 2012)

• Record Type: Journal Article
• Authors: Kardaras, Constantinos; Platen, Eckhard
• Is Part Of: Mathematical finance. Volume 23:Number 3(2013:Jul.)
• Page Start: 579
• Page End: 590
• Publication Date: 2012-02-03
• Subjects: Business mathematics -- Periodicals; 332
• DOI: 10.1111/j.1467-9965.2011.00511.x
• Languages: English
• ISSNs: 0960-1627

Abstract

<abstract abstract-type="main" xml:lang="en"> <title> <x xml:space="preserve">Abstract</x> </title> <p>A financial market model with general semimartingale asset–price processes and where agents can only trade using no‐short‐sales strategies is considered. We show that wealth processes using continuous trading can be approximated very closely by wealth processes using simple combinations of buy‐and‐hold trading. This approximation is based on controlling the <italic>proportions</italic> of wealth invested in the assets. As an application, the utility maximization problem is considered and it is shown that optimal expected utilities and wealth processes resulting from continuous trading can be approximated arbitrarily well by the use of simple combinations of buy‐and‐hold strategies.</p> </abstract>