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|  | Garschhammer, C. and R. Zagst |
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Ein stochastisches Modell zur Ertragsoptimerung bei Versicherungen
in: Spremann, K. (Ed.), Versicherung im Umbruch - Werte schaffen, Risiken managen,
Kunden gewinnen, 415-442, Springer Verlag, Heidelberg
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| Abstract: |
Trotz augenscheinlicher Ähnlichkeit von Versicherungsrisiken und Kapitalrisiken können letztere
aufgrund geringerer Transaktionskosten, leichterer Diversifikation und Möglichkeiten der Absicherung durch
Derivate i.a. einfacher gehandhabt werden als Versicherungsrisiken. Eine rechtzeitige Planung unter Einbezug
der möglichen zukünftigen Entwicklungen ist daher unumgänglich. Neben der Einrichtung entsprechender
Frühwarnsysteme, die entstehende Risiken rechtzeitig aufzeigen und der Einführung adäquater
Risikomanagementprozesse und Guidelines sollte die komplette Kapitalallokation eines Unternehmens anhand
eines ausgewogenen bzw. optimierten Chancen-Risikoprofils erfolgen. Grundlage dieses Artikels ist das Modell
von Schnieper (1997), in dem der Zusammenhang zwischen dem Gewinn eines Versicherungsunternehmens und
seinen Kapitalbedürfnissen untersucht wird. Wir nehmen jedoch an, dass das Unternehmenskapital gewissen
Unsicherheiten wie z.B. Preis- oder Zinsänderungen unterliegt und dass es das Ziel des Unternehmens ist, den
risikoadjustierten Ertrag zu maximieren. In diesem Sinne verallgemeinert das hier vorgeschlagene stochastische
Modell das Modell von Schnieper und erlaubt es, eine explizite Lösung für die optimale Struktur des
Unternehmensportfolios sowie die zu wählende Anlage- und Rückversicherungspolitik anzugeben.
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| | Kallsen, J. |
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Sigma-Localization and Sigma-Martingales
Theory of Probability and its Applications, 48: 152-163
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| Abstract: |
This paper introduces the concept of sigma-localization, which is a generalization of
localization in the general theory of stochastic processes. The sigma-localized class derived
from the set of martingales is the class of sigma-martingales, which plays an important
role in mathematical finance. These processes and the corresponding sigma-martingale
measures are considered in detail. By extending the stochastic integral with respect to
compensated random measures, a canonical representation of sigma-martingales as for local
martingales is derived.
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| | Kallsen, J. and C. Kühn |
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Pricing Derivatives of American and Game Type in Incomplete Markets
Finance and Stochastics, 8: 261-284
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| Abstract: |
In this paper the neutral valuation approach is applied to American and game options
in incomplete markets. Neutral prices occur if investors are utility maximizers and
if derivative supply and demand are balanced. Game contingent claims are derivative
contracts that can be terminated by both counterparties at any time before expiration.
They generalize American options where this right is limited to the buyer of the claim.
In turns out that as in the complete case, the price process of American and game
contingent claims corresponds to a Snell envelope or to the value of a Dynkin game,
respectively.
On the technical level, an important role is played by sigma-sub- and sigma-supermartingales.
We characterize these processes in terms of semimartingale characteristics.
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| | Schöttle, K. and R. Werner |
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Improving "the Most General Methodology to Create a Valid Correlation Matrix"
Risk Analysis IV, Management Information Systems, Vol 9, Wessex (2004)
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| Abstract: |
Jaeckel and Rebonato develop two different methods of creating valid correlation matrices: construction by hypersphere decomposition and by singular value (i.e. spectral) decomposition. Although both methods yield satisfactory results in practice, from a mathematical point of view, they both share some theoretical drawbacks.
Using results from semidefinite programming (SDP) we give the most general problem formulation to compute valid correlation matrices. We present numerical results which prove that these SDPs are rather easily solvable with efficient solvers for SDP problems (e.g. PENNON, see [3]). In contrast to Higham we do not find numerical difficulties in solving the stated SDP problems. We close the article with two more very important features which have been neglected in literature so far. First, regularity and second, control of the condition number of the resulting correlation matrix are easily guaranteed by linear SDPconstraints. Numerical experiments show that these additional constraints do not harm the efficient numerical solution.
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| | Zagst, R. and J. Roth |
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Three-Factor Defaultable Term Structure Models
International Journal of Pure and Applied Mathematics, Vol. 17, No. 2, 2004, 249-285
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| Abstract: |
Based on the model of Schmid & Zagst (2000) for pricing defaultable bonds, we develop a modified
hybrid model which allows for correlations between the different factors. To embed this new model, we compare it
to an intensity-based model according to Duffee (1996) and a structural model based on Bakshi et al. (2001). The
parameters of the different models are estimated by the Kalman filter methodology as described in Schmid
(2002). Based on these estimates we compare different quantities with regard to the performance of the models.
First we consider the absolute pricing errors in- and out-of-sample, then we examine a regression test to explain
the changes of the yields. Further we discuss the sensitivities of the several factors on the spreads and finally we
compare the observable default rates to the filtered firmspecific factors. We can show that our new model
provides the best results in comparison.
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