NO CLE - Standard of Value

The federal code (and similarly state law) define "insolvent" as a "financial condition such that the sum of [the] entity's debts is greater than all of [the] entity's property, at a fair valuation..." 11 U.S.C. § 101(32)(A). Fair valuation is not defined in the bankruptcy code. How does fair valuation for solvency differ from fair market value which is used for valuation for income tax purposes? Or fair value which is used in shareholder oppression matters? What are the implications of using trading prices for the assets versus assuming continuity of operating within the existing legal entity? What are the differences it could create in measuring the cost of capital? Or contingent liabilities?