Existence of Optimal Strategies Based on Specified Information, for a Class of Stochastic Decision Problems

Abstract

The existence of admissible strategies $\gamma ( \cdot , \cdot )$ minimizing a function $E\int_0^1 {c(t,x,\gamma (t,x))dt} $ is studied, with $x = x( \cdot ,\omega )$ a continuous stochastic process, and admissible strategies defined as those utilizing a specified pattern of information about x, here described by $\sigma $-algebras $G_t $ included in the “past” $\{ {x(s),s \leqq t} \}$. Conclusion: Moment conditions on x, growth conditions on c, and continuity of c in its third variable (the control) ensure that an optimal admissible strategy exists. The method of proof depends on properties of conditional expectations, and on a variant of a general Filippov (or implicit functions) lemma due to McShane and Warfield.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 164 citations exist upstream.