BFS 2002

Poster Presentation

Dynamic minimization of worst conditional expectation of shortfall under partial information

Jun Sekine

In a complete financial market model, in which the price processes of risky assets are described as diffusions with unobservable drifts, we treat the ``shortfall-risk'' minimization problem at the terminal date for a seller of a derivative security $F$. We adopt the worst conditional expectation of the shortfall as the measure of this risk, ensuring that the minimized risk satisfies some desirable properties as the dynamic measure of risk after Cvitanic and Karatzas (1999). The terminal value of the optimized portfolio is a binary functional, dependent on $F$ and $\widehat{Z}_T$, the projection of the Radon-Nikodym density of the minimal local martingale measure onto the available information for the hedger. In particular, we observe that there exists a positive number $x^*$, which is less than the replicating cost $x^F$ of $F$, and that the strategy minimizing the expectation of the shortfall is optimal if the hedger's capital lies in $[x^*,x^F]$.