Optimal Reinsurance Under Distortion Risk Measures and Expected Value Premium Principle for Reinsurer

This paper discusses optimal reinsurance strategy by minimizing insurer's risk under one general risk measure:Distortion risk measure.The authors assume that the reinsurance premium is determined by the expected value premium principle and the retained loss of the insurer is an increasing function of the initial loss.An explicit solution of the insurer's optimal reinsurance problem is obtained.The optimal strategies for some special distortion risk measures,such as value-at-risk(VaR) and tail value-at-risk(TVaR),are also investigated.

Influence of FCA Welding Process Parameters on Distortion of 409M Stainless Steel for Rail Coach Building

The influence of flux cored arc welding （FCAW） process parameters such as welding current, travel speed, voltage and CO2 shielding gas flow rate on bowing distortion of 409M ferritic stainless steel sheets of 2 mm in thickness was discussed. The bowing distortions of the welded plates were measured using a simple device called profile tracer. An experimental regression equation was developed to predict the bowing distortion and with this equation, it is easy to select optimized process parameters to achieve minimum bowing distortion. It is revealed that the FCAW process parameters have significant influence on bead profile and the bowing distortion.

Tail Distortion Risk Measure for Portfolio with Multivariate Regularly Variation

For the multiplicative background risk model,a distortion-type risk measure is used to measure the tail risk of the portfolio under a scenario probability measure with multivariate regular variation.In this paper,we investigate the tail asymptotics of the portfolio loss ∑_(i=1)^(d)R_(i)S,where the stand-alone risk vector R=(R_(1),...,R_(d))follows a multivariate regular variation and is independent of the background risk factor S.An explicit asymptotic formula is established for the tail distortion risk measure,and an example is given to illustrate our obtained results.

Speech distortion measure based on auditory properties

The Perceptual Spectrum Distortion (PSD), based on auditory properties of human being, is presented to measure speech distortion. The PSD measure calculates the speech distortion distance by simulating the auditory properties of human being and converting short-time speech power spectrum to auditory perceptual spectrum. Preliminary simulative experiments in comparison with the Itakura measure have been done. The results show that the PSD measure is a perferable speech distortion measure and more consistent with subjective assessment of speech quality.

Now decision theory

The spirit of now in nowcasting suggests expanding the current to include the near future.Decision theory is then developed by incorporating the consequences of actions into the present.With the future falling into the present discounting it is no longer permitted.Value functions are then observed to be determinate only up to scale and shift that are then locked down by fixing values arbitrarily in two selected states,much like declaring water to freeze and boil at zero and a hundred degrees celsius.The locked down value functions associated policy functions are seen to exist in decision contexts in where the only time is now.Examples are studied in univariate and multivariate dimensions for the decision state space and the dimension of shocks delivering state transitions.The policy functions are expanded from realisitic training sets to the full state space using Gaussian Process Regression.They are implemented on real data with reported performances.

Optimal reinsurance designs based on risk measures:a review

Reinsurance is an effective way for an insurance company to control its risk.How to design an optimal reinsurance contract is not only a key topic in actuarial science,but also an interesting research question in mathematics and statistics.Optimal reinsurance design problems can be proposed from different perspectives.Risk measures as tools of quantitative risk management have been extensively used in insurance and finance.Optimal reinsurance designs based on risk measures have been widely studied in the literature of insurance and become an active research topic.Different research approaches have been developed and many interesting results have been obtained in this area.These approaches and results have potential applications in future research.In this article,we review the recent advances in optimal reinsurance designs based on risk measures in static models and discuss some interesting problems on this topic for future research.

Measure distorted arrival rate risks and their rewards

Risks embedded in asset price dynamics are taken to be accumulations of surprise jumps.A Markov pure jump model is formulated on making variance gamma parameters deterministic functions of the price level.Estimation is done by matrix exponentiation of the transition rate matrix for a continuous time finite state Markov chain approximation.The motion is decomposed into a space dependent drift and a space dependent martingale component.Though there is some local mean reversion in the drift,space dependence of the martingale component renders the dynamics to be of the momentum type.Local risk is measured using market calibrated measure distortions that introduce risk charges into the lower and upper prices of two price economies.These risks are compensated by the exponential variation of space dependent arrival rates.Estimations are conducted for the S&P 500 index(SPX),the exchange traded fund for the financial sector(XLF),J.P.Morgan stock prices(JPM),the ratio of JPM to XLF,and the ratio of XLF to SPX.

Remarks on Equality of Two Distributions under Some Partial Orders

In this note we establish some appropriate conditions for stochastic equality of two random vari- ables/vectors which are ordered with respect to convex ordering or with respect to supermodular ordering. Multivariate extensions of this result are also considered.