INFORMATION AND OPTIMAL INVESTMENT IN DEFAULTABLE ASSETS

Giulia Di Nunno () and Steffen Sjursen ()
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Giulia Di Nunno: Center of Mathematics for Applications, University of Oslo, P.O. Box 1053 Blindern, N-0316 Oslo, Norway;
Steffen Sjursen: Center of Mathematics for Applications, University of Oslo, P.O. Box 1053 Blindern, N-0316 Oslo, Norway

International Journal of Theoretical and Applied Finance (IJTAF), 2014, vol. 17, issue 08, 1-27

Abstract: We study optimal investment in an asset subject to risk of default for investors that rely on different levels of information. The price dynamics can include noises both from a Wiener process and a Poisson random measure with infinite activity. The default events are modeled via a counting process in line with large part of the literature in credit risk. In order to deal with both cases of inside and partial information we consider the framework of the anticipating calculus of forward integration. This does not require a priori assumptions typical of the framework of enlargement of filtrations. We find necessary and sufficient conditions for the existence of a locally maximizing portfolio of the expected utility at terminal time. We consider a large class of utility functions. In addition we show that the existence of the solution implies the semi-martingale property of the noises driving the stock. Some discussion on unicity of the maxima is included.

Keywords: Information; optimal portfolio; default risk; insider; forward integrals (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1142/S0219024914500502

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