Optimal Numeraires for Risk Measures

Can the usage of a risky numeraire with a greater than risk free expected return reduce the capital requirements in a solvency test? I will show that this is not the case. In fact, under a reasonable technical condition, there exists no optimal numeraire which yields smaller capital requirements than any other numeraire.

Importance of Institutional Development for Western Balkan Countries

Western Balkan countries comprises following entities: Bosnia and Hercegovina, Serbia and Montenegro, Kosovo and Metohija, Albania and Macedonia. Even there are just four sovereign(internationaly recognised) states among those entities, number of different names (8) shows to us all fragmentation and tendencies toward further dissolution of this region to increasing number of small and weak states. Tendencies that are shown in WB region are quite different from those in other transition countries in Europe. Instead of cooperation in economic, financial and all other important fields, like Visegrad group countries did in nineties and strenghten their negotiation position compared with the EU, WB countries try to flatter to EU member states and to build their better position through deterioration of the position of other regional states. On the internal plan, all WB countries are still rely on weak institutional capacity - mechanisms that enables governments non-transparent behavior, manipulation with judicial system and judges, selective implementation of the laws, very high and resistant level of corruption in all social and economic fields, surviving of organised crime structures which are very often related to government officials at all levels of authority etc. Integration of WB countries in the EU will be very long term and difficult process as the precondition for that will be building of effective institutional mechanisms that could provide governance comparative with other transition countries and in more distant future with European mature market economies. It isimportant also to establish efficient regional cooperation and to increase level of income and competitiveness to cope with the competition from EU. Experiences from other Balkan countires should be useful for WB region - Greek's as one old member state and Romania's and Bulgaria's as candidate meber states. WB countries expect to have greater understanding of EU officials for the very serious problems that have to be resolved and it is out of question that without important support from outside WB it will be impossible to do so.

Shot noise of charge and spin transport in a junction with a precessing molecular spin

Magnetic molecules and nanomagnets can be used to influence the electronic transport in mesoscopic junction. In a magnetic field the precessional motion leads to resonances in the dc- and ac-transport properties of a nanocontact, in which the electrons are coupled to the precession. Quantities like the dc-conductance or the ac-response provide valuable information like the level structure and the coupling parameters. Here, we address the current noise properties of such contacts. This encompasses the charge current and spin-torque shot noise, which both show a step-like behavior as functions of bias voltage and magnetic field. The charge current noise shows pronounced dips around the steps, which we trace back to interference effects of electron in quasienergy levels coupled by the molecular spin precession. We show that some components of the noise of the spin-torque currents are directly related to the Gilbert damping and, hence, are experimentally accessible. Our results show that the noise characteristics allow to investigate in more detail the coherence of spin transport in contacts containing magnetic molecules.Comment: 10 pages, 8 figure, published versio

Polynomial Diffusions and Applications in Finance

This paper provides the mathematical foundation for polynomial diffusions. They play an important role in a growing range of applications in finance, including financial market models for interest rates, credit risk, stochastic volatility, commodities and electricity. Uniqueness of polynomial diffusions is established via moment determinacy in combination with pathwise uniqueness. Existence boils down to a stochastic invariance problem that we solve for semialgebraic state spaces. Examples include the unit ball, the product of the unit cube and nonnegative orthant, and the unit simplex.Comment: This article is forthcoming in Finance and Stochastic

Regularity of finite-dimensional realizations for Evolution Equations

We show that a continuous local semiflow of $C^k$-maps on a finite-dimensional $C^k$-manifold M can be embedded into a local $C^k$-flow on M under some weak (necessary) assumptions. This result is applied to an open problem in [fil/tei:01]. We prove that finite-dimensional realizations for interest rate models are highly regular objects, namely given by submanifolds M of $D(A^{\infty})$, where A is the generator of a strongly continuous semigroup

Option Pricing with Orthogonal Polynomial Expansions

We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein-Stein, and Hull-White models, for which we provide numerical case studies. We find that our polynomial option price series expansion performs as efficiently and accurately as the Fourier transform based method in the nested affine cases. We also derive and numerically validate series representations for option Greeks. We depict an extension of our approach to exotic options whose payoffs depend on a finite number of prices.Comment: forthcoming in Mathematical Finance, 38 pages, 3 tables, 7 figure