## Contributed Talk

### Decision Risk Reductions for Stock Indices

Wolfgang Stummer

We model the dynamics $X_t$ of a stock index as a non--lognormally--distributed generalization of the geometric Brownian motion. In detail, $X_t$ is supposed to be a weak solution of a one-dimensional stochastic differential equation of the form
$$dX_t = b(X_t) dt + \sigma X_t dW_t,$$
with volatility $\sigma > 0$ and Brownian motion $W_t$. For a dichotomous Bayesian decision problem concerning the size of the drift $b$, we investigate the (average) reduction of decision risk that can be obtained by observing the path of $X$. We also show some connections with relative entropy and with contingent claim pricing.