A General Maximum Principle for Anticipative Stochastic Control and Applications to Insider Trading

Giulia Di Nunno (), Olivier Menoukeu Pamen (), Bernt Øksendal () and Frank Proske ()
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Giulia Di Nunno: University of Oslo, CMA, Department of Mathematics
Olivier Menoukeu Pamen: University of Oslo, CMA, Department of Mathematics
Bernt Øksendal: University of Oslo, CMA, Department of Mathematics
Frank Proske: University of Oslo, CMA, Department of Mathematics

Chapter Chapter 7 in Advanced Mathematical Methods for Finance, 2011, pp 181-221 from Springer

Abstract: Abstract In this paper we suggest a general stochastic maximum principle for optimal control of anticipating stochastic differential equations driven by a Lévy-type noise. We use techniques of Malliavin calculus and forward integration. We apply our results to study a general optimal portfolio problem of an insider. In particular, we find conditions on the insider information filtration which are sufficient to give the insider an infinite wealth. We also apply the results to find the optimal consumption rate for an insider.

Keywords: Anticipative stochastic control; Maximum principle; Malliavin calculus; Insider trading; Forward integrals; Skorokhod integrals; 93E20; 91G80; 60G51; 60H10 (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18412-3_7

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DOI: 10.1007/978-3-642-18412-3_7

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