# Tag Info

It's been quite a while since I did this stuff, but I'll add my input. Please correct me if appropriate. $\{H < T\} = \{ \sup_{0\leq s \leq T} (S_{0} + \sigma B_{s}) > a \} = \{\sup_{0 \leq s \leq T} B_s > \frac{a-S_0}{\sigma}\}$. Set $\mu := \frac{a-S_0}{\sigma}$ and $M_{T} := \sup_{0 \leq s \leq T} B_{s}$. Then, $P(\{H < T\} = P(\{M_T > ... 0 The risk aversion coefficient is also referred to as the Arrow-Pratt risk aversion index. When λ is small (i.e., the aversion to risk is low), the pen- alty from the contribution of the portfolio risk is also small, leading to more risky portfolios. Conversely, when λ is large, portfolios with more exposures to risk become more highly penalized. If we ... 2 It could be much more simple: if you use the method of moments (MM) then you estimate the mean and the variance and for example the kurtosis of your sample. Then you fit the parameters to these statistics. Alternatively you use maximum-likelihood (MLE). For MM: from wikipedia you get the mean and the variance. In your notation you can fit$b = \bar{r}\$ so ...