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Comparison principle approach to utility maximization

Peter Imkeller, Victor Nzengang (2015)

Banach Center Publications

We consider the problem of optimal investment for maximal expected utility in an incomplete market with trading strategies subject to closed constraints. Under the assumption that the underlying utility function has constant sign, we employ the comparison principle for BSDEs to construct a family of supermartingales leading to a necessary and sufficient condition for optimality. As a consequence, the value function is characterized as the initial value of a BSDE with Lipschitz growth.

Complete q -order moment convergence of moving average processes under ϕ -mixing assumptions

Xing-Cai Zhou, Jin-Guan Lin (2014)

Applications of Mathematics

Let { Y i , - ∞ < i < ∞ } be a doubly infinite sequence of identically distributed ϕ -mixing random variables, and { a i , - ∞ < i < ∞ } an absolutely summable sequence of real numbers. We prove the complete q -order moment convergence for the partial sums of moving average processes X n = ∑ i = - ∞ ∞ a i Y i + n , n ≥ 1 based on the sequence { Y i , - ∞ < i < ∞ } of ϕ -mixing random variables under some suitable conditions. These results generalize and complement earlier results.

Componentwise concave copulas and their asymmetry

Fabrizio Durante, Pier Luigi Papini (2009)

Kybernetika

The class of componentwise concave copulas is considered, with particular emphasis on its closure under some constructions of copulas (e.g., ordinal sum) and its relations with other classes of copulas characterized by some notions of concavity and/or convexity. Then, a sharp upper bound is given for the L ∞ -measure of non-exchangeability for copulas belonging to this class.

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