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Viable Insider Markets

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  • Olfa Draouil
  • Bernt {O}ksendal

Abstract

We consider the problem of optimal inside portfolio $\pi(t)$ in a financial market with a corresponding wealth process $X(t)=X^{\pi}(t)$ modelled by \begin{align}\label{eq0.1} \begin{cases} dX(t)&=\pi(t)X(t)[\alpha(t)dt+\beta(t)dB(t)]; \quad t\in[0, T] X(0)&=x_0>0, \end{cases} \end{align} where $B(\cdot)$ is a Brownian motion. We assume that the insider at time $t$ has access to market information $\varepsilon_t>0$ units ahead of time, in addition to the history of the market up to time $t$. The problem is to find an insider portfolio $\pi^{*}$ which maximizes the expected logarithmic utility $J(\pi)$ of the terminal wealth, i.e. such that $$\sup_{\pi}J(\pi)= J(\pi^{*}), \text {where } J(\pi)= \mathbb{E}[\log(X^{\pi}(T))].$$ The insider market is called \emph{viable} if this value is finite. We study under what inside information flow $\mathbb{H}$ the insider market is viable or not. For example, assume that for all $t

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  • Olfa Draouil & Bernt {O}ksendal, 2018. "Viable Insider Markets," Papers 1801.03720, arXiv.org.
  • Handle: RePEc:arx:papers:1801.03720
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    References listed on IDEAS

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    1. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 263-286, July.
    2. Stefan Ankirchner & Peter Imkeller, 2007. "Financial Markets with Asymmetric Information: Information Drift, Additional Utility and Entropy," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 1, pages 1-21, World Scientific Publishing Co. Pte. Ltd..
    3. Caroline Hillairet, 2005. "Existence Of An Equilibrium With Discontinuous Prices, Asymmetric Information, And Nontrivial Initial Σ‐Fields," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 99-117, January.
    4. Jan Ubøe & Bernt Øksendal & Knut Aase & Nicolas Privault, 2000. "White noise generalizations of the Clark-Haussmann-Ocone theorem with application to mathematical finance," Finance and Stochastics, Springer, vol. 4(4), pages 465-496.
    5. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," SFB 373 Discussion Papers 1998,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. Giulia Di Nunno & Thilo Meyer-Brandis & Bernt Øksendal & Frank Proske, 2006. "Optimal portfolio for an insider in a market driven by Levy processes," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 83-94.
    7. José Corcuera & Peter Imkeller & Arturo Kohatsu-Higa & David Nualart, 2004. "Additional utility of insiders with imperfect dynamical information," Finance and Stochastics, Springer, vol. 8(3), pages 437-450, August.
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