A General Stochastic Calculus Approach to Insider Trading |
| |
Authors: | Francesca Biagini Bernt Øksendal |
| |
Institution: | (1) Department of Mathematics, University of Bologna, Piazza di Porta S. Donato 5, I-40127 Bologna, Italy;(2) Center of Mathematics for Applications (CMA), Department of Mathematics, University of Oslo, Box 1053 Blindern, N-0316 Oslo, Norway;(3) Norwegian School of Economics and Business Administration, Helleveien 30, N-5045 Bergen, Norway |
| |
Abstract: | The purpose of this paper is to present a general stochastic calculus
approach to insider trading. We consider a market driven by a standard Brownian
motion $B(t)$ on a filtered probability space $\displaystyle
(\Omega,\F,\left\{\F\right\}_{t\geq 0},P)$ where the coefficients are
adapted to a filtration ${\Bbb G}=\left\{\G_t\right\}_{0\leq t\leq T}$,
with $\F_t\subset\G_t$ for all $t\in 0,T]$, $T>0$ being a fixed terminal time.
By
an {\it insider} in this market we
mean a person who has access to a filtration (information)
$\displaystyle{\Bbb H}=\left\{\H_t\right\}_{0\leq t\leq T}$ which is strictly
bigger than the filtration
$\displaystyle{\Bbb G}=\left\{\G_t\right\}_{0\leq t\leq T}$.
In this context an insider strategy is represented by an
$\H_t$-adapted process
$\phi(t)$ and we interpret all anticipating integrals as
the forward integral defined in
23] and 25].
We consider an optimal portfolio problem with
general utility for an insider with access to a general information
$\H_t \supset\G_t$ and show that if
an optimal insider portfolio $\pi^*(t)$ of this problem exists, then
$B(t)$ is an $\H_t$-semimartingale, i.e. the enlargement
of filtration property holds. This is a converse of previously
known results in this field.
Moreover, if $\pi^*$ exists
we obtain an explicit expression in terms of $\pi^*$ for the
semimartingale decomposition of $B(t)$ with respect to $\H_t$.
This is a generalization
of results in 16], 20] and 2]. |
| |
Keywords: | Forward integral Skorohod integral Wick product Insider trading Utility function |
本文献已被 SpringerLink 等数据库收录! |
|