References
- Aase, K.K. (2004a). Borch, Karl Henrik (1919 - 1986). Encyclopedia of Actuarial Science 1, 191–195.
- Aase, K.K. (2004b). Optimal risk sharing. Encyclopedia of Actuarial Science 3, 1212–1215.
- Albrecher, H., Beirlant, J. & Teugels, J.L. (2017). Reinsurance: actuarial and statistical aspects. West Sussex: Wiley.
- Arrow, K. (1963). Uncertainty and the welfare economics of medical care. American Economic Review 53, 941–973.
- Artzner, P., Delbaen, F., Eber, J.M. & Heath, D. (1999). Coherent measures of risk. Mathematical Finance 9, 203–228. doi: 10.1111/1467-9965.00068
- Asimit, A.V. & Boonen, T.J. (2018). Insurance with multiple insurers: a game-theoretic approach. European Journal of Operational Research 267(2), 778–790. doi: 10.1016/j.ejor.2017.12.026
- Asimit, A.V., Gao, T., Hu, J. & Kim, E.S. (2018). Optimal risk transfer: a numerical optimisation approach. North American Actuarial Journal. to appear.
- Borch, K. (1960a). An attempt to determine the optimum amount of stop loss reinsurance. Transactions of the 16th International Congress of Actuaries 1, 597–610. Reprinted as Chapter 1 in Borch (1974).
- Borch, K. (1960b). The safety loading of reinsurance premiums. Skandinavisk Aktuarietidskrift 0, 163–184. Reprinted as Chapter 9 in Borch (1974).
- Borch, K. (1960c). Reciprocal reinsurance treaties. ASTIN Bulletin 1(4), 170–191. Reprinted as Chapter 4 in Borch (1974). doi: 10.1017/S0515036100009557
- Borch, K. (1962). Equilibrium in a reinsurance market. Econometrica 30, 424–444. Reprinted as Chapter 10 in Borch (1974). doi: 10.2307/1909887
- Borch, K. (1969). The optimal reinsurance treaty. ASTIN Bulletin 5(2), 293–297. Reprinted as Chapter 2 in Borch (1974). doi: 10.1017/S051503610000814X
- Borch, K. (1974). The mathematical theory of insurance: an annotated selection of papers on insurance. Published 1960-1972. Lexington, MA: Lexington Books.
- Bühlmann, H. (1970). Mathematical methods in risk theory. Heidelberg: Springer-Verlag.
- Cai, J. & Weng, C. (2016). Optimal reinsurance with expectile. Scandinavian Actuarial Journal 2016(7), 624–645. doi: 10.1080/03461238.2014.994025
- Cai, J., Liu, H. & Wang, R. (2017). Pareto-optimal reinsurance arrangements under general model settings. Insurance: Mathematics and Economics 77, 24–37.
- Cheung, K.C., Chong, W.F., Elliott, R. & Yam, S.C.P. (2015a). Disappointment aversion premium principle. ASTIN Bulletin 45(3), 679–702. doi: 10.1017/asb.2015.12
- Cheung, K.C., Chong, W.F. & Yam, S.C.P. (2015b). The optimal insurance under disappointment theories. Insurance: Mathematics and Economics 64, 77–90.
- Deprez, O. & Gerber, H.U. (1985). On convex principles of premium calculation. Insurance: Mathematics and Economics 4, 179–189.
- D'Ortona, A.E. & Marcarelli, G. (2017). Optimal proportional reinsurance from the point of view of cedent and reinsurer. Scandinavian Actuarial Journal 2017(4), 366–375. doi: 10.1080/03461238.2016.1148627
- Fischer, T. (2003). Risk capital allocation by coherent risk measures based on one-sided moments. Insurance: Mathematics and Economics 32, 135–146.
- Föllmer, H. & Schied, A. (2002). Convex measures of risk and trading constraints. Finance and Stochastics 6(4), 429–447. doi: 10.1007/s007800200072
- Föllmer, H. & Schied, A. (2016). Stochastic finance: an introduction in discrete time, 4th ed. Walter de Gruyter: Berlin.
- Gerber, H.U. (1978). Pareto-optimal risk exchanges and related decision problems. ASTIN Bulletin 10, 25–33. doi: 10.1017/S0515036100006310
- Gerber, H.U. (1981). The Esscher premium principle: a criticism. Comment. ASTIN Bulletin 12, 139–140. doi: 10.1017/S0515036100007078
- Gerber, H.U. & Pafumi, G. (1998). Utility functions: from risk theory to finance. North American Actuarial Journal 2(3), 74–100. doi: 10.1080/10920277.1998.10595728
- Golubin, A.Y. (2008). Pareto optimality and equilibrium in an insurance market. ASTIN Bulletin 38(2), 441–459. doi: 10.1017/S0515036100015245
- Goovaerts, M.J., De Vylder, F. & Haezendonck, J. (1984). Insurance Premiums: Theory and Applications. North Holland: Amsterdam.
- Goovaerts, M.J., Dhaene, J. & Rachedi, O. (2010). Actuarial premium principles. Encyclopedia of Quantitative Finance 1, 7–12.
- Kaluszka, M. & Okolewski, A. (2008). An extension of Arrow's result on optimal reinsurance contract. The Journal of Risk and Insurance 75(2), 275–288. doi: 10.1111/j.1539-6975.2008.00260.x
- Kiesel, S. & Rüschendorf, L. (2013). On the optimal reinsurance problem. Applicationes Mathematicae 40, 259–280. doi: 10.4064/am40-3-1
- Lo, A. (2017). A Neyman-Pearson perspective on optimal reinsurance with constraints. ASTIN Bulletin 47(2), 467–499. doi: 10.1017/asb.2016.42
- Lo, A. & Tang, Z. (2018). Pareto-optimal reinsurance policies in the presence of individual risk constraints. Annals of Operations Research, in press.
- McNeil, A.J., Frey, R. & Embrechts, P. (2015). Quantitative risk management: concepts, techniques and tools. Revised edition. Princeton, NJ: Princeton University Press.
- Moffet, D. (1979). The risk sharing problem. Geneva Papers on Risk and Insurance 11, 5–13.
- Newey, W. & Powell, J. (1987). Asymmetric least squares estimation and testing. Econometrica 55(4), 819–847. doi: 10.2307/1911031
- Promislow, S.D. & Young, V.R. (2005). Unifying framework for optimal insurance. Insurance: Mathematics and Economics 36, 347–364.
- Raviv, A. (1979). The design of an optimal insurance policy. The American Economic Review 69(1), 84–96.
- Young, V.R. (1999). Optimal insurance under Wang's premium principle. Insurance: Mathematics and Economics 25, 109–122.
- Young, V.R. (2004). Premium principles. Encyclopedia of Actuarial Science 3, 1322–1331.