 Our analysis allowed us to conclude that under some mild assumptions on the market model and the random time, these structures  will remain valid on the one hand.
<meaning-changed>  Our analysis allowed us to conclude that under some mild assumptions on the market model and the random time, these structures  will remain valid on the one hand.
 Our analysis allowed us to conclude that under some mild assumptions on the market model and the random time, these structures conditions will remain valid on the one hand.