Das zweiändrige Wahrscheinlichkeitsgesetz der Abweichungen der Prämienreserve eines Bestandes von Versicherungen mit verschiedenen Auflösungsmöglichkeiten. I
Das zweiändrige Wahrscheinlichkeitsgesetz der Abweichungen der Prämienreserve eines Bestandes von Versicherungen mit verschiedenen Auflösungsmöglichkeiten. II
Did bank capital regulation exacerbate the subprime mortgage crisis?
Die Zufallsverträge in der Wahrscheinlichkeitsrechnung. I
Die Zufallsverträge in der Wahrscheinlichkeitsrechnung. II
Discrete Lundberg-type bounds with actuarial applications
Different kinds of renewal equations repeatedly arise in connection with renewal risk models and variations. It is often appropriate to utilize bounds instead of the general solution to the renewal equation due to the inherent complexity. For this reason, as a first approach to construction of bounds we employ a general Lundberg-type methodology. Second, we focus specifically on exponential bounds which have the advantageous feature of being closely connected to the asymptotic behavior (for large...
Discrete time infinite horizon risk sensitive portfolio selection with proportional transaction costs
Long run risk sensitive portfolio selection is considered with proportional transaction costs. In the paper two methods to prove existence of solutions to suitable Bellman equations are presented. The first method is based on discounted cost approximation and requires uniform absolute continuity of iterations of transition operators of the factor process. The second method is based on uniform ergodicity of portions of the capital invested in assets and requires additional assumptions concerning...
Dynamic dependence ordering for Archimedean copulas and distorted copulas
This paper proposes a general framework to compare the strength of the dependence in survival models, as time changes, i. e. given remaining lifetimes , to compare the dependence of given , and given , where . More precisely, analytical results will be obtained in the case the survival copula of is either Archimedean or a distorted copula. The case of a frailty based model will also be discussed in details.
Dynamic monetary risk measures for bounded discrete-time processes.
Dynamic reforming of a quasi pay-as-you-go social security system within a discrete stochastic multidimensional framework using optimal control methods
In many western economies, the phenomenon of ageing population implies that the large Pay-As-You-Go (PAYGO) social security system will run into several severe financial difficulties. In that direction, this paper constructs a discrete-time stochastic model for a quasi PAYGO social security system to allow the potential accumulation of a special (contingency) fund, which can oscillate so as to absorb fluctuations in the various system parameters involved. The basic difference equation is analytically...
Dynamic term structure modelling with default and mortality risk: new results on existence and monotonicity
This paper considers dynamic term structure models like the ones appearing in portfolio credit risk modelling or life insurance. We study general forward rate curves driven by infinitely many Brownian motions and an integer-valued random measure, generalizing existing approaches in the literature. A precise characterization of absence of arbitrage in such markets is given in terms of a suitable criterion for no asymptotic free lunch (NAFL). From this, we obtain drift conditions which are equivalent...
Estimating the conditional tail expectation in the case of heavy-tailed losses.
Estimation of a Regression Function on a Point Process and its Application to Financial Ruin Risk Forecast
2000 Mathematics Subject Classification: Primary 60G55; secondary 60G25.We estimate a regression function on a point process by the Tukey regressogram method in a general setting and we give an application in the case of a Risk Process. We show among other things that, in classical Poisson model with parameter r, if W is the amount of the claim with finite espectation E(W) = m, Sn (resp. Rn) the accumulated interval waiting time for successive claims (resp. the aggregate claims amount) up to the...
Estimation of hidden Markov models for a partially observed risk sensitive control problem
This paper provides a summary of our recent work on the problem of combined estimation and control of systems described by finite state, hidden Markov models. We establish the stochastic framework for the problem, formulate a separated control policy with risk-sensitive cost functional, describe an estimation scheme for the parameters of the hidden Markov model that describes the plant, and finally indicate how the combined estimation and control problem can be re-formulated in a framework that...
Evaluating Total Operational Value and Associated Risks of Financial Holding Companies in Taiwan
Extremal moment methods and stochastic orders.
From isotonic Banach functionals to coherent risk measures
Coherent risk measures [ADEH], introduced to study both market and nonmarket risks, have four characteristic properties that lead to the term “coherent” present in their name. Coherent risk measures regarded as functionals on the space have been extensively studied [De] with respect to these four properties. In this paper we introduce CRM functionals, defined as isotonic Banach functionals [Al], and use them to characterize coherent risk measures on the space as order opposites of CRM functionals....
Generalized CreditRisk+ model and applications
In the paper we give a mathematical overview of the CreditRisk+ model as a tool used for calculating credit risk in a portfolio of debts and suggest some other applications of the same method of analysis.
Generalized duration measures in a risk immunization setting. Implementation of the Heath-Jarrow-Morton model
The aim of this paper is to set different lower bounds on the change of the expected net cash flow value at time H > 0 in general term structure models, referring to the studies of Fong and Vasiček (1984), Nawalkha and Chambers (1996), and Balbás and Ibáñez (1998) among others. New immunization strategies are derived with new risk measures: generalized duration and generalized M-absolute of Nawalkha and Chambers, and exponential risk measure. Furthermore, examples of specific one-factor HJM models...
Geometric properties of multivariate correlation in de Finetti's approach to insurance theory.