8,146 research outputs found
A 3d-3d appetizer
We test the 3d-3d correspondence for theories that are labelled by Lens
spaces. We find a full agreement between the index of the 3d "Lens
space theory" and the partition function of complex Chern-Simons
theory on . In particular, for , we show how the familiar
partition function of Chern-Simons theory arises from the index of a free
theory. For large , we find that the index of becomes a constant
independent of . In addition, we study on the squashed
three-sphere . This enables us to see clearly, at the level of partition
function, to what extent complex Chern-Simons theory can be
thought of as two copies of Chern-Simons theory with compact gauge group .Comment: 27 pages. v2: misprints corrected, references added. v3: misprints
corrected, a clarification adde
Three-Benchmarked Risk Minimization for Jump Diffusion Markets
The paper discusses the problem of hedging not perfectly replicable contingent claims by using a benchmark, the numerraire portfolio, as reference unit. The proposed concept of benchmarked risk minimization generalizes classical risk minimization, pioneered by Follmer, Sondermann and Schweizer. The latter relies on a quadratic criterion, requesting the square integrability of contingent claims and the existence of an equivalent risk neutral probability measure. The proposed concept of benchmarked risk minimization avoids these restrictive assumptions. It employs the real world probability measure as pricing measure and identifies the minimal possible price for the hedgable part of a contingent claim. Furthermore, the resulting benchmarked profit and loss is only driven by nontraded uncertainty and forms a martingale that starts at zero. Benchmarked profit and losses, when pooled and sufficiently independent, become in total negligible. This property is highly desirable from a risk management point of view. It is making a symptotically benchmarked risk minimization the least expensive method for pricing and hedging for an increasing number of not fully replicable benchmarked contingent claims.incomplete market; pricing; hedging; numeraire portfolio; risk minimization; benchmark approach
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