I'm not 100 % operational since query failed to be executed but saiku now loads.
First point : tomcat/saiku/catalina.out contains the interesting log information for debugging. Second point : location string in the saiku configuration did point to a missing file, that didn't help. Third point : dimension tables should be mentionned in Mondrian's XML (the correct version follows).
<Schema name="New Schema1">
<Cube name="companies_cube" visible="true" cache="true" enabled="true">
<Table name="fact_companies">
</Table>
<Dimension type="TimeDimension" visible="true" foreignKey="date_id" highCardinality="false" name="date">
<Hierarchy name="Date" visible="true" hasAll="true" allMemberName="all dates" allMemberCaption="all dates" allLevelName="all dates">
<Table name="dim_date">
</Table>
<Level name="Year" visible="true" table="dim_date" column="year" nameColumn="year" type="String" uniqueMembers="false" levelType="TimeYears" hideMemberIf="Never">
</Level>
<Level name="Month" visible="true" table="dim_date" column="month" nameColumn="month" type="String" uniqueMembers="false" levelType="TimeMonths" hideMemberIf="Never">
</Level>
<Level name="Date" visible="true" table="dim_date" column="date" nameColumn="date" type="String" uniqueMembers="false" levelType="TimeDays" hideMemberIf="Never">
</Level>
</Hierarchy>
</Dimension>
<Dimension type="StandardDimension" visible="true" foreignKey="sector_id" highCardinality="false" name="Sector">
<Hierarchy name="Sector" visible="true" hasAll="true" allMemberName="all sector" allMemberCaption="all sector" allLevelName="all sector" primaryKey="sector_id">
<Table name="dim_sector" alias="">
</Table>
<Level name="Sector" visible="true" table="dim_sector" column="sector_id" nameColumn="sector" type="String" uniqueMembers="false" levelType="Regular" hideMemberIf="Never">
</Level>
</Hierarchy>
</Dimension>
<Measure name="count companies" column="count" aggregator="sum" visible="true">
</Measure>
</Cube>
</Schema>