An important and often neglected aspect in probabilistic planning is how to account for different attitudes towards risk in the process. In goal-driven problems, modeled as Shortest Stochastic Path (ssp) problems, risk arises from the uncertainties on future events and how they can lead to goal states. An ssp agent that minimizes the expected accumulated cost is considered a risk-neutral agent, while with a different optimization criterion it could choose between two extreme attitudes: risk-aversion or risk-prone. In this work we consider a Risk Sensitive ssp (called rs-ssp) that uses an expected exponential utility parameterized by the risk factor $\backslashlambda$ that is used to define the agent’s risk attitude. Moreover, a $\backslashlambda$-value is feasible if it admits a policy with finite expected cost. There are several algorithms capable of determining an optimal policy for rs-ssp s when we fix a feasible value for $\backslashlambda$. However, so far, there has been only one approach to find an extreme $\backslashlambda$-feasible i.e., an extreme risk-averse policy. In this work we propose and compare new approaches to finding the extreme feasible $\backslashlambda$ value for a given rs-ssp, and to return the corresponding extreme risk-averse policy. Experiments on three benchmark domains show that our proposals outperform previous approach, allowing the solution of larger problems.