Kohatsu-Higa, Arturo; Sulem, Agnès Utility maximization in an insider influenced market. (English) Zbl 1136.91450 Math. Finance 16, No. 1, 153-179 (2006). Summary: We study a controlled stochastic system whose state is described by a stochastic differential equation with anticipating coefficients. This setting is used to model markets where insiders have some influence on the dynamics of prices. We give a characterization theorem for the optimal logarithmic portfolio of an investor with a different information flow from that of the insider. We provide explicit results in the partial information case that we extend in order to incorporate the enlargement of filtration techniques for markets with insiders. Finally, we consider a market with an insider who influences the drift of the underlying price asset process. This example gives a situation where it makes a difference for a small agent to acknowledge the existence of an insider in the market. Cited in 22 Documents MSC: 91G10 Portfolio theory 91B70 Stochastic models in economics 91B16 Utility theory 60H30 Applications of stochastic analysis (to PDEs, etc.) 60H05 Stochastic integrals 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 93E20 Optimal stochastic control PDFBibTeX XMLCite \textit{A. Kohatsu-Higa} and \textit{A. Sulem}, Math. Finance 16, No. 1, 153--179 (2006; Zbl 1136.91450) Full Text: DOI Link References: [1] Biagini F., Appl. Math. Optim. 52 pp 167– (2005) [2] DOI: 10.1007/s00780-003-0119-y · Zbl 1064.60087 · doi:10.1007/s00780-003-0119-y [3] DOI: 10.1016/S0165-1889(97)00065-1 · Zbl 0902.90031 · doi:10.1016/S0165-1889(97)00065-1 [4] DOI: 10.1142/S0219024901000961 · Zbl 1154.91542 · doi:10.1142/S0219024901000961 [5] DOI: 10.1111/1467-9965.00011 · Zbl 1071.91017 · doi:10.1111/1467-9965.00011 [6] Karatzas I., Adv. Appl. Probab. 28 pp 1095– (1996) [7] Kohatsu-Higa A., Stochastic Processes and Applications to Math. Fin. (2006) [8] Nualart D., The Malliavin Calculus and Related Topics (1995) · Zbl 0837.60050 · doi:10.1007/978-1-4757-2437-0 [9] DOI: 10.1007/BF00353876 · Zbl 0629.60061 · doi:10.1007/BF00353876 [10] B.Oksendal, and A.Sulem(2004 ): Partial Observation in an Anticipative Environment , 59 , 355 -375 . [11] DOI: 10.1007/BF01195073 · Zbl 0792.60046 · doi:10.1007/BF01195073 [12] DOI: 10.1016/0304-4149(95)93237-A · Zbl 0840.60052 · doi:10.1016/0304-4149(95)93237-A [13] Russo F., Stoch. Stoch. Rep. 70 pp 1– (2000) · Zbl 0981.60053 · doi:10.1080/17442500008834244 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.