A strong law of large numbers for trimmed sums, with applications to generalized St. Petersburg games

Extending a result of Einmahl, Haeusler and Mason (1988), a characterization of the almost sure asymptotic stability of lightly trimmed sums of upper order statistics is given when the right tail of the underlying distribution with positive support is surrounded by tails that are regularly varying with the same index. The result is motivated by applications to cumulative gains in a sequence of generalized St. Petersburg games in which a fixed number of the largest gains of the player may be withheld.