86,550 research outputs found
On a conjecture about enumerating -free posets
Recently, Kitaev and Remmel posed a conjecture concerning the generating
function for the number of unlabeled -free posets with respect to number
of elements and number of minimal elements. In this paper, we present a
combinatorial proof of this conjecture
Martingale Optimal Transport and Robust Hedging in Continuous Time
The duality between the robust (or equivalently, model independent) hedging
of path dependent European options and a martingale optimal transport problem
is proved. The financial market is modeled through a risky asset whose price is
only assumed to be a continuous function of time. The hedging problem is to
construct a minimal super-hedging portfolio that consists of dynamically
trading the underlying risky asset and a static position of vanilla options
which can be exercised at the given, fixed maturity. The dual is a
Monge-Kantorovich type martingale transport problem of maximizing the expected
value of the option over all martingale measures that has the given marginal at
maturity. In addition to duality, a family of simple, piecewise constant
super-replication portfolios that asymptotically achieve the minimal
super-replication cost is constructed
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