  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 $t<T$ the
insider knows the value of $B(t+\epsilon_t)$, where $t + \epsilon_t \geq T$
converges monotonically to $T$ from above as $t$ goes to $T$ from below. Then
(assuming that the insider has a perfect memory) at time $t$ she has the inside
information $\mathcal{H}_t$, consisting of the history $\mathcal{F}_t$ of
$B(s); 0 \leq s \leq t$ plus all the values of Brownian motion in the interval
$[t+\epsilon_t, \epsilon_0]$, i.e. we have the enlarged filtration
\begin{equation}\label{eq0.2} \mathbb{H}=\{\mathcal{H}_t\}_{t\in[0.T]},\quad
\mathcal{H}_t=\mathcal{F}_t\vee\sigma(B(t+\epsilon_t+r),0\leq r \leq
\epsilon_0-t-\epsilon_t), \forall t\in [0,T]. \end{equation} Using forward
integrals, Hida-Malliavin calculus and Donsker delta functionals we show that
if $$\int_0^T\frac{1}{\varepsilon_t}dt=\infty,$$ then the insider market is not
viable.
