The Completion of Real-Asset Markets by Options

We combine the theory of finite-dimensional lattice subspaces and the theory of regular values for maps between smooth manifolds in order to study the completion of real asset markets by options. The strike asset of the options is supposed to be a nominal asset. The main result of the paper is like in the case of the completion of a nominal asset market by options that if the strike asset of the options is the riskless asset, then the completion of a real asset market is generically equal to ℝ

No arbitrage pricing of non-marketed claims in multi-period markets

In this paper, we modify the arbitrage-free interval of prices for a non-marketed contingent claim in the finite event-tree model of financial markets, according to the perfect hedging approach being well-known for the two-period model. We prove the existence of solution to the corresponding seller's and buyer's price problem for such a claim under no-arbitrage prices for the marketed contracts and we show that each of these problems can be solved by decomposing it into a finite number of one-period linear programming problems solved backwards. Finally, we indicate that the set of the no-arbitrage prices for a non-marketed contingent claim is the interval of the real numbers whose supremum and infimum is the seller's and the buyer's price of the claim, respectively. The determination of the set of no-arbitrage prices for a non-marketed contingent claim is related to the utility pricing of such a claim.contingent claims; seller price; buyer price; contingent claim pricing; no-arbitrage pricing; non-marketed claims; multi-period markets; finite event-tree modelling; financial markets; hedging.

Restricted Coherent Risk Measures and Actuarial Solvency

We prove a general dual representation form for restricted coherent risk measures, and we apply it to a minimization problem of the required solvency capital for an insurance company

Risk measures in ordered normed linear spaces with non-empty cone-interior

In this paper, we use tools from the theory of partially ordered normed linear spaces, especially the bases of cones. This work extends the well-known results for convex and coherent risk measures. Its linchpin consists in the replacement of the riskless bond by some interior point in the cone of the space of risks, which stands as the alternative numeraire.Base of a cone Well-based cones Numeraire asset Coherent and convex risk measures Representability of risk measures

When does financial leverage create economic value?

This paper addresses an overriding question in the theory of capital structure concerning how external financing contributes to economic value creation. Adjusted Present Value rule for capital-investment decisions (see [5], [6]) is used as performance metric of added value. This frame spotlights the contribution to added value attributable to each financing source. We show that levered project and financial leverage add value, at any debt level, if Net Present Value of the investment project and Net Present Value of debt are both positive. However if Net Present Value of debt is negative, external financing destroys economic value and should be taken at the minimum necessary