S. E. Posner

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The authors use risk-neutral option pricing theory to value the guaranteed minimum death benefit (GMDB) in variable annuities (VAs) and some recently introduced mutual funds. A variety of death benefits, such as returnof-premium, rising floors, and “ratches,” are analyzed. Specifically, the authors compute the fair insurance risk fee, charged to assets,(More)
Rates of convergence for nearest neighbor estimation are established in a general framework in terms of metric covering numbers of the underlying space. Our first result is to find explicit finite sample upper bounds for the classical independent and identically distributed (i.i.d.) random sampling problem in a separable metric space setting. The(More)
We nd tight upper and lower bounds on the growth rate for the covering numbers of functions of bounded variation in the L 1 metric in terms of all the relevant constants. We also nd upper and lower bounds on covering numbers for general function classes over the family of L 1 (dP) metrics, in terms of a scale-sensitive combinatorial dimension of the(More)
Let . . . be an arbitrary random process taking values in a totally bounded subset of a separable metric space. Associated with we observe drawn from an unknown conditional distribution ( = ) with continuous regression function ( ) = [ = ]. The problem of interest is to estimate based on and the data ( ) . We construct appropriate data-dependent nearest(More)
The authors construct a class of elementary nonparametric output predictors of an unknown discrete-time nonlinear fading memory system. Their algorithms predict asymptotically well for every bounded input sequence, every disturbance sequence in certain classes, and every linear or nonlinear system that is continuous and asymptotically time-invariant,(More)
We consider the problem of learning of an arbitrary function selected from the non-smooth class of functions that are of bounded variation. Bounds on the prediction errors resulting from sequential type algorithms are achieved for various scenarios. It is shown that for any algorithm there exists a sequence of samples and a function that results in a unit(More)
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