A subordinator is a process with independent, stationary non-negative increments. We ca view this process as the kumulative distribution function of a random measure on an interval. Dividing this maasure by its total mass yields a probability measure. Random measures constructed this way are the subject of this thesis. They arise as limit measures associated with lengths of cycles of random permutations, urn models and lenghts of excursions of diffusion processes. The thesis contains results about the joint distribution of the $n$ largest atoms of such random measure. The results are applied to obtain information on the distribution of the largest cycle in a random prrmutation and the distribution of the duration of exursions of a Bessel process.

The thesis explores the effects of buyer-supplier networks and crossholdings on the pricing of financial instruments. We propose a structural model of firm dependence in a vertically connected network of firms based on cash flow transfers between the buyers and the suppliers. We prove that financial market completeness in a closed network economy depends only on the topology of the network. We develop analytical formulae for zero-coupon corporate debt, credit default swaps and collateralized debt obligations by decomposing the risk structure into that arising from buy-supply orders and that arising from exogenous sources of firm income. We test the empirical validity of the model on the subcontractors' network of the SwissAir Group. To deal with dynamic defaults, we develop a fast algorithm for computation of default times of multiple firms in the structural network model constructed in the previous section. The algorithm uses a multivariate extension of Fortet's equation and the structure of Toeplitz matrices to significantly improve the computation time. The algorithm is then applied to firm survival probability computation and zero coupon bond pricing with dynamic defaults. In the third part of the dissertation we consider an economy of firms with crossheld securities. The value of the debt contract in such a network depends on the value of other debt contracts. This has the potential to induce contagion effects. The article proposes a Monte-Carlo algorithm to solve the valuation problem of debt prices in an economy with crossholdings. As the number of firms in network increases, debt yields increase only to a certain level, which we interprete as a measure of balance-sheet contagion. An increase in variance of the fundamental assets of one firm is almost totally absorbed within the debt yield of that firm. On the other hand, heterogeneity of debt principals has the potential to induce large contagion effects.