A note on admissibility when the credit line is infinite

Abstract

In the context of expected utility maximization for utilities defined on the whole real line, we define a new class of admissible strategies in terms of dynamic bounds on losses under the historical measure . More precisely, the loss control is given by a -martingale which is compatible with the preferences of the investor. The main result is the Ansel–Stricker-type Lemma 3.3 which shows that the admissible strategies are supermartingales under all sigma-martingale measures with finite relative entropy, therefore, allowing for a duality theory for the optimization problem.

Keywords:

• utility maximization
• non-locally bounded semimartingale
• investment opportunity
• supermartingale property
• duality theory

2000 Mathematics Subject Classification::

• primary 60G48
• 60G44
• 49N15
• 91B28
• secondary 46E30
• 46N30
• 91B16

Acknowledgements

SB was supported in part by MIUR Grant PRIN-2008 YYYBE4. MS was supported in part by the National Science Foundation under Grants 0802681 and DMS 0908441.

Notes

^1. [email protected]