In this paper, in order to model breach of contract risk, we design and value a bundled option that is composed of contract abandonment and price renegotiation. We show numerically that the bundled option is more valuable for the contract than either of the options, ie, contract abandonment and price renegotiation, in isolation. This value increases monotonically as the spot price becomes more ...

The optimal length r(n) of a sequence in [1, n] containing no 3term arithmetic progression is determined for several new values of n and some results relating to the subadditivity of r are obtained. We also prove a particular case of a conjecture of Szekeres. A subsequence S = (a1, a2, . . . , ak) of the sequence 〈n〉 = (1, 2, . . . , n) containing no three terms ap, aq, and ar for which aq − ap...

Compound Poisson population models are particular conditional branching process models. A formula for the transition probabilities of the backward process for general compound Poisson models is verified. Symmetric compound Poisson models are defined in terms of a parameter θ ∈ (0,∞) and a power series φ with positive radius r of convergence. It is shown that the asymptotic behavior of symmetric...

Since combinational auctions allow bidders to bid on any combination of goods, bid data can be of exponential size. To combat this problem, restrictions have been proposed limiting the number of bundles a bidder is allowed to bid on (as in FCC Auction #31). We describe a new combinatorial auction format that restricts bidders to submit a fixed number of “matrix bids with order”. The advantage o...

Capacity appears in electrostatics as a characteristic of a body made of conducting material: it is the maximal charge that can be put on this body so that the electric potential of the field created by this charge is bounded by 1. In 1924 Norbert Wiener introduced capacity in mathematics as a positive function of compact sets. It is not additive as a measure but subadditive. Starting with Wien...

We study mechanisms for combinatorial auctions that are simultaneously incentive compatible (IC), envy free (EF) and efficient in settings with capacitated valuations — a subclass of subadditive valuations introduced by Cohen et al. [4]. Capacitated agents have valuations which are additive up to a publicly known capacity. The main result of Cohen et al. [4] is the assertion that the Vickrey-Cl...

Copyright q 2010 Dongseung Kang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We investigate the generalized Hyers-Ulam-Rassias stability problem in quasi-β-normed spaces and then the stability by using a subadditive function f...