Before revision:  The public information generated by the financial assets, and a larger flow of information containing additional knowledge about a death time(random time /horizon) of an insured. By expanding the filtration, the death uncertainty and its entailed risk are fully considered without any mathematical restriction.
After revision:  The public information generated by the financial assets, and a larger flow of information containing additional knowledge about a random time. This random time can represent many economic and financial settings, such as the default time of a firm for credit risk, and the death time of an insured for life insurance. By using the expansion of filtration, the death uncertainty and its entailed risk are fully considered without any mathematical restriction.