Premium Calculation by Transforming the Layer Premium Density

By Shaun S. Wang. 1996

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Citations in the corpus

Implicit Quantile Networks for Distributional Reinforcement Learning (2018, background): “Such a function h is known as a distortion risk measure, as it distorts the cumulative probabilities of the random variable (Wang, 1996).”
On the one parameter unit-Lindley distribution and its associated regression model for proportion data (2018, background): “ 2 The c.d.f. of the unit-Lindley is bounded for > 3=2 as follows. x F (x j ) 1 exp x 1 x : Therefore the c.d.f. can be used to dene new premium by distorting survival function (see Wang, 1996). Proposition 3 The p.d.f. of the unit-Lindley is log-concave for all 0 < x < 1 if 3 2 . P”
Coherent measures of risk in everyday market practice (2007, background): “Spectral measures of risk turned out to be strictly related to the class of distortion risk measures introduced in actuarial mathematics in 1996 by Wang (1996) in a different setting.”
Natural Hedging of Life and Annuity Mortality Risks (2007, unknown): “Wang (1996, 2000, 2001) has developed a method of pricing risks that unifies financial and insurance pricing theories.”
Optimal Capital Allocation Principles (2005, unknown): “See Wang (1996), Acerbi (2002), or Dhaene et al. (2006).”
Asymptotics for Risk Capital Allocations Based on Conditional Tail Expectation (2011, unknown): “It belongs to both the distorted and weighted risk measures (see Wang, 1996; Dhaene et al., 2006; Furman and Zitikis, 2008a).”
After VaR: The Theory, Estimation, and Insurance Applications of Quantile-Based Risk Measures (2006, unknown): “They were introduced by Denneberg (1990) and Wang (1996) and have been applied to a wide variety of insurance problems, most particularly to the determination of insurance premiums.”
Analytical Evaluation of Economic Risk Capital for Portfolios of Gamma Risks (2001, background): “It is easy to show that (1.6) ( )RaC X g F x dx1a Xa 0 = - 3 #6 6@ @ identifies the RaC functional with a member of the class of distortion pricing principles in Wang (1996).”
A FORM OF MULTIVARIATE PARETO DISTRIBUTION WITH APPLICATIONS TO FINANCIAL RISK MEASUREMENT (2016, background): “(4.3) We note in passing that both VaR and CTE are distorted as well as weighted risk measures (see, respectively, Wang, 1996; and Furman and Zitikis, 2008a).”
Robust distortion risk measures (2022, unknown): “…distortion risk measures to illustrate our results: the dual power distortion with parameter 𝛽 > 0 , 𝑔(𝑥) = 1 − (1 − 𝑥) 𝛽 , and 𝛾(𝑢) = 𝛽𝑢 𝛽−1 ; (2) the Wang transform (Wang, 1996) with parameter 0 < 𝑞 0 < 1 , where Φ and 𝜙 denote the standard normal distribution and its density,…”
Some New Classes of Consistent Risk Measures (2004, background): “As in Bühlmann (1970)(see alsoGerber, 1979, 1985; Kaas et al., 2001), suppose that one approaches a premium calculation from top-down, for instance by considering a ruin probability model for the determination of the portfolio premium on the top level.”
Securitization of Mortality Risks in Life Annuities (2005, unknown): “Securitization Reinsurance Publicly traded or private placement”
Expected shortfall and beyond (2002, background): “(iii) Formulas like (3.4) can be traced back a long time in the actuarial literature (cf. Wang, 1996, and the references therein).”