There exist several characterizations of concavity for univariate functions. One of them states that a function is concave if and only if it has nonincreasing differences. This definition provides a natural generalization of concavity for multivariate functions called inframodularity....

In combinatorial auctions the pricing problem is of main concern since it is the means by which the auctioneer signals the result of the auction to the participants. In order for the auction to be regarded as fair among the various participants the price signals should be such that a participant...

The thesis considers an investor's problem of optimal consumption and portfolio choice in a financial market. The model used for the financial market is the semimartingales model. The thesis shows that an optimal solution to this problem exists, even if the investor is contrained in the...

Ambiguity, also called Knightian or model uncertainty, is a key feature in financial modeling. A recent paper by Maccheroni et al. (2004) characterizes investor preferences under aversion against both risk and ambiguity. Their result shows that these preferences can be numerically represented in...

We use the duality in linear programming to solve the problem of optimal contracts with moral hazards. We show the importance of allowing the partners to throw away outputs under some contingencies. A two-step procedure is used to find the optimal contracts. The first step minimizes the loss...