293 research outputs found
Local properties of accessible injective operator ideals
No full textIn addition to Pisier’s counterexample of a non-accessible maximal Banach ideal, we will give a large class of maximal Banach ideals which are accessible. The first step is implied by the observation that a “good behaviour” of trace duality, which is canonically induced by conjugate operator ideals can be extended to adjoint Banach ideals, if and only if these adjoint ideals satisfy an accessibility condition (theorem 3.1). This observation leads in a natural way to a characterization of accessible injective Banach ideals, where we also recognize the appearance of the ideal of absolutely summing operators (prop. 4.1). By the famous Grothendieck inequality, every operator from L_1 to a Hilbert space is absolutely summing, and therefore our search for such ideals will be directed towards Hilbert space factorization—via an operator version of Grothendieck’s inequality (lemma 4.2). As a consequence, we obtain a class of injective ideals, which are “quasi-accessible”, and with the help of tensor stability, we improve the corresponding norm inequalities, to get accessibility (theorem 4.1 and 4.2). In the last chapter of this paper we give applications, which are implied by a non-trivial link of the above mentioned considerations to normed products of operator ideals
Some open problems in the geometry of operator ideals. The principle of local reflexivity for maximal Banach ideals
No full textOn normed products of operator ideals which contain L2 as a factor
No full textWe investigate quasi-Banach operator ideal products (A ? B,A ? B) which contain (L2,L2) as a factor. In particular, we ask for conditions which guarantee that A ? B is even a norm if each factor of the product is a 1-Banach ideal. In doing so, we reveal the strong influence of the existence of such a norm in relation to the accessibility of the product ideal and the structure of its factors
Extension of finite rank operators and operator ideals with the property (I)
No full textAbstract. We present criteria and related techniques which help to decide whether the adjoint operator ideal (A * , A * ) of an injective and totally accessible maximal Banach ideal (A, A) is itself also totally accessible. This approach (which involves the transfer of the principle of local reflexivity to operator ideals) is based on the extension of finite rank operators, viewed as elements of the adjoint ideal (A * , A * ). Using the local properties (I) and (S) of the corresponding product ideal A * • L∞, these methods even enable us to show that L∞ and L 1 cannot be totally accessible -answering an open question of Defant and Floret
On utility-based super-replication prices of contingent claims with unbounded payoffs
No full textThe authors gratefully acknowledge support from EPSRC grant number GR/S80202/01. Consider a financial market in which an agent trades with utility-induced restrictions on wealth. For a utility function which satisfies the condition of reasonable asymptotic elasticity at -oo, we prove that the utility-based superreplication price of an unbounded (but sufficiently integrable) contingent claim is equal to the supremum of its discounted expectations under pricing measures with finite loss-entropy. For an agent whose utility function is unbounded from above, the set of pricing measures with finite loss-entropy can be slightly larger than the set of pricing measures with finite entropy. Indeed, the former set is the closure of the latter under a suitable weak topology. Central to our proof is a proof of the duality between the cone of utility-based superreplicable contingent claims and the cone generated by pricing measures with finite loss-entropy. © Applied Probability Trust 2007.</p
Notes and Comments: The numeraire portfolio in financial markets modeled by a multi-dimensional jump diffusion process
No full textIn continuous time, we study a financial market which is free of arbitrage opportunities but incomplete under the physical probability measure P. Thus one has several choices of equivalent martingale measures. In the present paper, the (unique) martingale measure P* is studied which is defined by the concept of the numeraire portfolio. The choice of P* can be justified by a change of numeraire in place of a change of measure
Restructuring counterparty credit risk
No full textWe introduce an innovative theoretical framework for the valuation and replication of derivative transactions between defaultable entities based on the principle of arbitrage freedom. Our framework extends the traditional formulations based on credit and debit valuation adjustments (CVA and DVA). Depending on how the default contingency is accounted for, we list a total of ten different structuring styles. These include bi-partite structures between a bank and a counterparty, tri-partite structures with one margin lender in addition, quadri-partite structures with two margin lenders and, mostimportantly, configurations where all derivative transactions are cleared through a central counterparty clearing house (CCP). We compare the various structuring styles under a number of criteria including consistency from an accounting standpoint, counterparty risk hedgeability, numerical complexity, transaction portability upon default, induced behaviour and macro-economic impact of the implied wealth allocation
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