Optimal insurance in the presence of insurer’s loss limit

Charting a Course on the Islamic Finance Ocean: A Survey of Islamic Insurance Literatures

“…Over the years, continuous writings and practical experiences of stakeholders have paid for its standardization at both market and academic levels. Thus, enough literature is available on its technical and core operational aspects of underwriting (Schultz & Bardwell, 1959;Bickelhaupt, 1983;Mehr, 1986;Rejda, 1989;Beekman, 1990) and rating (pricing) (Arrow, 1963(Arrow, , 1971(Arrow, , 1973(Arrow, , 1974Raviv, 1979;Bühlmann, 1985Bühlmann, , 1997Trowbridge, 1989;Schweizer, 2001;Whelan, 2002;Light, 2004;Cummins & Mahul, 2002D'arcy, 2005;Laeven & Goovaerts, 2007;Zhou et al, 2010;Bernard et al, 2012). Regulations are well documented through ages globally.…”

“…Excellent academic researchers, such as Arrow (1963Arrow ( , 1971Arrow ( , 1974, Raviv (1979), Bühlmann (1985), Briys, Dionne, and Eeckhoudt (1989), Rejda (1989), Green, Trieschmann, and Gustavson (1992), Luan (2001), Mahul (2002, 2004), Liu and Yang (2004), Laeven and Goovaerts (2008), Karni (2007), Zhou, W. Wu, and C. Wu (2010), Walhin and Paris (1999), Bernard, He, Yan, and Zhou (2012), have developed various models of rating based on various mathematical and statistical methods. Similarly, British government has invested regulations in the standardization of insurance business such as life assurance Gambling act of 1774 and marine insurance act of 1906 to mention some.…”

Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle

“…Borch [1] (and also Arrow [4]) showed that, subject to a budget constraint, the stop-loss policy is an optimal reinsurance contract for the ceding company when the risk is measured by variance (or by a utility function). Reinsurance optimization problems involving premium constraint were also considered in Gajek and Zagrodny [10], Zhou, et al [28], Zheng and Cui [21], Cui, et al [22] and Cheung and Lo [18]. Cheung, et al [29] introduced a reinsurer's probabilistic benchmark constraint of his potential loss.…”

The bounds of premium and optimality of stop loss insurance under uncertain random environments

“…Pliska and Ye (2007) considered optimal insurance and consumption rules for a wage earner whose lifetime was random. Zhou et al (2010) considered the optimal insurance problem when the insurer had a loss limit constraint. Lu et al (2012) derived an optimal insurance treaty when the insured faced multiple sources of risk.…”