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Several facts about Theodor Wittstein, Gaetano Balducci, and some expressions of the net single premiums under their mortality assumption

The mathematical essence in life insurance spins around the search of the nu\-me\-ri\-cal characteristics of the random variables $T_x$, $ν^{T_x}$, $T_xν^{T_x}$, etc., where $ν$ (deterministic) denotes the discount multiplier and $T_x$ (random) is the future lifetime of an in\-di\-vi\-dual being of $x\in\{0,\,1,\,\ldots\}$ years old. This work provides some historical facts about T. Wittstein and G. Balducci and their mortality assumption. We also develop some formulas that make it easier to compute the moments of the mentioned random variables assuming that the survival function is interpolated according to Balducci's assumption. Derived formulas are verified using some hypothetical mortality data.