Asymptotic solutions of diffusion models for risk reserves.
Asymptotics of riskless profit under selling of discrete time call options
A discrete time model of financial market is considered. In the focus of attention is the guaranteed profit of the investor which arises when the jumps of the stock price are bounded. The limit distribution of the profit as the model becomes closer to the classic model of geometrical Brownian motion is established. It is of interest that the approximating continuous time model does not assume any such profit.
Bank valuation and its connections with the subprime mortgage crisis and basel II capital accord.
Bounds for Value at Risk - The Approach Based on Copulas with Homogeneous Tails.
Bounds of Ruin Probabilities for Insurance Companies in the Presence of Stochastic Volatility on Investments⋆⋆⋆
In this work we consider a model of an insurance company where the insurer has to face a claims process which follows a Compound Poisson process with finite exponential moments. The insurer is allowed to invest in a bank account and in a risky asset described by Geometric Brownian motion with stochastic volatility that depends on an external factor modelled as a diffusion process. By using exponential martingale techniques we obtain upper and lower...
Building bridges between Mathematics, Insurance and Finance
Paul Embrechts is Professor of Mathematics at the ETH Zurich specializing in Actuarial Mathematics and Quantitative Risk Management. Previous academic positions include the Universities of Leuven, Limburg and London (Imperial College). Dr. Embrechts has held visiting professorships at several universities, including the Scuola Normale in Pisa (Cattedra Galileiana), the London School of Economics (Centennial Professor of Finance), the University of Vienna, Paris 1 (Panthéon-Sorbonne), theNationalUniversity...
Chance constrained problems: penalty reformulation and performance of sample approximation technique
We explore reformulation of nonlinear stochastic programs with several joint chance constraints by stochastic programs with suitably chosen penalty-type objectives. We show that the two problems are asymptotically equivalent. Simpler cases with one chance constraint and particular penalty functions were studied in [6,11]. The obtained problems with penalties and with a fixed set of feasible solutions are simpler to solve and analyze then the chance constrained programs. We discuss solving both problems...
Comparing convolutions with Dhaene-Vandebroek and De Pril's recursions from a computational point of view.
Compatibility between pricing rules and risk measures: The CCVaR.
Compound Compound Poisson Risk Model
2000 Mathematics Subject Classification: 60K10, 62P05.The compound Poisson risk models are widely used in practice. In this paper the counting process in the insurance risk model is a compound Poisson process. The model is called Compound Compound Poisson Risk Model. Some basic properties and ruin probability are given. We analyze the model under the proportional reinsurance. The optimal retention level and the corresponding adjustment coefficient are obtained. The particular case of the Pólya-Aeppli...
Conditional value-at-risk bounds for compound Poisson risks and a normal approximation.
Continuous time linear-fractional programming. The minimum-risk approach
Continuous time linear-fractional programming. The minimum-risk approach
Continuous time portfolio selection under conditional capital at risk.
Continuous-time mean–risk portfolio selection
Contributions to the credibility theory.
Copula-based grouped risk aggregation under mixed operation
This paper deals with the problem of risk measurement under mixed operation. For this purpose, we divide the basic risks into several groups based on the actual situation. First, we calculate the bounds for the subsum of every group of basic risks, then we obtain the bounds for the total sum of all the basic risks. For the dependency relationships between the basic risks in every group and all of the subsums, we give different copulas to describe them. The bounds for the aggregated risk under mixed...
Core solutions and nash equilibria in noncooperative games with a measure space of players
The paper deals with noncooperative games in which players constitute a measure space. Strategy profiles that are equal almost everywhere are assumed to have the same interactive effects. Under these circumstances we explore links between core solutions and Nash equilibria. Conditions are given which guarantee that core outcomes must be Nash equilibria and vice versa. The main contribution are results on nonemptieness of the core.
Das Hattendorffsche Risiko kontinuierlicher Versicherungen mit mehrfachen Auflösungsmöglichkeiten
Das jährliche mathematische Risiko der Versicherungen, bei welchen zwei von einander verschiedene Ereignisse die vorzeitige Auflösung herbeiführen können