This note gives a simple proof of the existence and monotonicity of optimal debt contracts in simple models of borrowing and lending with ex−post asymmetric information, risk−averse agents and heterogeneous beliefs. Our argument is based on the concept of nondecreasing rearrangement and on a supermodular version of Hardy−Littlewood inequality. Citation: Renou, Ludovic and Guillaume Carlier, (20...

1.1. Plancherel measures. Given a finite group G, by the corresponding Plancherel measure we mean the probability measure on the set G∧ of irreducible representations of G which assigns to a representation π ∈ G∧ the weight (dim π)/|G|. For the symmetric group S(n), the set S(n)∧ is the set of partitions λ of the number n, which we shall identify with Young diagrams with n squares throughout th...

We consider scenarios in which long sequences of data are analyzed and subsequences must be traced that are monotone and maximum, according to some measure. A classical example is the online Longest Increasing Subsequence Problem for numeric and alphanumeric data. We extend the problem in two ways: (a) we allow data from any partially ordered set, and (b) we maximize subsequences using much mor...

We study the uctuations, in the large deviations regime, of the longest increasing subsequence of a random i.i.d. sample on the unit square. In particular, our results yield the precise upper and lower exponential tails for the length of the longest increasing subsequence of a random permutation. i=1 denote a sequence of i.i.d. random variables with marginal law on the unit square Q = 0; 1] 2. ...

This paper argues how transparency can increase trust and therefore indirectly enhances the results of Public Private Partnerships in complex construction projects. Complex construction projects, e.g. large infrastructure or urban development projects, with public client organizations and private contractors, frequently run into problems. Public Private Partnership projects are characterised by...

information asymmetry in stock market can increase the risk of investment which in turn increases the capital cost of firms. bhattacharya (1979) proposed a hypothesis that states dividend can act as a powerful signal in order to solve information asymmetry problem. we measured information asymmetry by lack of earnings transparency. therefore we examine the effect of earnings transparency on cap...

Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in O(n log n) time and space. Our goal in this paper is to reduce the space consumption while keeping the time complexity small. For √ n ≤ s ≤ n, we present algorithms that use O(s log n) bits and O( 1 s · n · log n) time for computing the length of a longe...

The deterministic space complexity of approximating the length of the longest increasing subsequence of a stream of N integers is known to be Θ̃( √ N). However, the randomized complexity is wide open. We show that the technique used in earlier work to establish the Ω( √ N) deterministic lower bound fails strongly under randomization: specifically, we show that the communication problems on which...

By reviewing Longest Increasing Subsequence (LIS) and Longest Common Subsequence (LCS), the Longest Common Increasing Subsequence (LCIS) problem is explored for two non-random input cases in details. Specifically, we designed two algorithms, one solving the input sequence scenario with the case that one sequence is ordered and duplicate elements are allowed in each of sequences, and the second ...

We consider the problem of :nding the longest increasing subsequence in a sliding window over a given sequence (LISW). We propose an output-sensitive data structure that solves this problem in time O(n log log n+OUTPUT) for a sequence of n elements. This data structure substantially improves over the na?@ve generalization of the longest increasing subsequence algorithm and in fact produces an o...