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Empirical evidence suggests that even those firms presumably most in need of monitoring-intensive financing (young, small, and innovative firms) have a multitude of bank lenders, where one may be special in the sense of relationship lending. However, theory does not tell us a lot about the economic rationale for relationship lending in the context of multiple bank financing. To fill this gap, we analyze the optimal debt structure in a model that allows for multiple but asymmetric bank financing. The optimal debt structure balances the risk of lender coordination failure from multiple lending and the bargaining power of a pivotal relationship bank. We show that firms with low expected cash-flows or low interim liquidation values of assets prefer asymmetric financing, while firms with high expected cash-flow or high interim liquidation values of assets tend to finance without a relationship bank.
Tractable hedging - an implementation of robust hedging strategies : [This Version: March 30, 2004]
(2004)
This paper provides a theoretical and numerical analysis of robust hedging strategies in diffusion–type models including stochastic volatility models. A robust hedging strategy avoids any losses as long as the realised volatility stays within a given interval. We focus on the effects of restricting the set of admissible strategies to tractable strategies which are defined as the sum over Gaussian strategies. Although a trivial Gaussian hedge is either not robust or prohibitively expensive, this is not the case for the cheapest tractable robust hedge which consists of two Gaussian hedges for one long and one short position in convex claims which have to be chosen optimally.
We modify the concept of LLL-reduction of lattice bases in the sense of Lenstra, Lenstra, Lovasz [LLL82] towards a faster reduction algorithm. We organize LLL-reduction in segments of the basis. Our SLLL-bases approximate the successive minima of the lattice in nearly the same way as LLL-bases. For integer lattices of dimension n given by a basis of length 2exp(O(n)), SLLL-reduction runs in O(n.exp(5+epsilon)) bit operations for every epsilon > 0, compared to O(exp(n7+epsilon)) for the original LLL and to O(exp(n6+epsilon)) for the LLL-algorithms of Schnorr (1988) and Storjohann (1996). We present an even faster algorithm for SLLL-reduction via iterated subsegments running in O(n*exp(3)*log n) arithmetic steps.