Mathematical foundation of the replicating portfolio approach

References

• Andreatta, G. & Corrad, S. (2003). Fair value of life liabilities with embedded options: an application to a portfolio of Italian insurance policies. Working Paper.
   Google Scholar
• Baione, F., De Angelis, P. & Fortunati, A. (2006). On a fair value model for participating life insurance policies. Investment Management and Financial Innovations 3(2), 408–421.
   Google Scholar
• Bauer, D., Bergmann, D. & Kiesel, R. (2010). On the risk-neutral valuation of life insurance contracts with numerical methods in view. Astin Bulletin 40(1), 65–95.
   Web of Science ®Google Scholar
• Bauer, D., Reuss, A. & Singer, D. (2012). On the calculation of the solvency capital requirement based on nested simulations. Astin Bulletin 42(2), 453–499.
   Web of Science ®Google Scholar
• Bernardo, A. & Ledoit, O. (2000). Gain, loss and asset pricing. Journal of Political Economy 108(1), 144–172.
   Web of Science ®Google Scholar
• Beutner, E., Pelsser, A. & Schweizer, J. (2013). Fast convergence of regress-later estimates in least squares Monte Carlo. Available at SSRN 328709.
   Google Scholar
• Beutner, E., Pelsser, A. & Schweizer, J. (2015). Theory and validation of replicating portfolios in insurance risk management. Available at SSRN 2557368.
   Google Scholar
• Biagini, S. & Pinar, M. (2013). The best gain-loss ratio is a poor performance measure. SIAM Journal on Financial Mathematics 4(1), 228–242.
   Web of Science ®Google Scholar
• Cambou, M. & Filipović, D., (2016). Replicating portfolio approach to capital calculation. Finance & Stochastics. Forthcoming. Available at SSRN 2763733.
   Web of Science ®Google Scholar
• Chen, W. & Skoglund, J. (2012). Cash flow replication with mismatch constraints. The Journal of Risk 14(4), 115–128.
   Web of Science ®Google Scholar
• Dalang, R., Morton, A. & Willinger, W. (1990). Equivalent martingale measures and no-arbitrage in stochastic securities market models. Stochastics and Stochastic Reports 29(2), 185–201.
   Google Scholar
• Daul, S. & Vidal, E., (2009). Replication of insurance liabilities. RiskMetrics 9(1), 79–96.
   Google Scholar
• Delbaen, F. & Schachermayer, W. (2006). The mathematics of arbitrage. Heidelberg: Springer.
   Google Scholar
• Dubrana, L. (2011). A formalized hybrid portfolio replication technique applied to participating life insurance portfolios. http://ssrn.com/abstract=1964464 [Accessed 14.09.2015].
   Google Scholar
• Dubrana, L. (2012). Modeling of variable annuity economic capital for market risk using a form of path-dependent Monte Carlo scenarios and a bump & revalue approach on greeks. Available at SSRN 2083621.
   Google Scholar
• EIOPA. (2014). The underlying assumptions in the standard formula for the solvency capital requirement calculation. https://eiopa.europa.eu [Accessed 25.07.2014].
   Google Scholar
• Gibbs, A. & Su, F. (2002). On choosing and bounding probability metrics. International and Statistical Review 70(3), 419–435.
   Web of Science ®Google Scholar
• Glasserman, P. & Yu, B. (2004). Simulation for American options: regression now or regression later. Monte Carlo and Quasi-Monte Carlo Methods 2002, 213–226.
   Google Scholar
• Hancock, J., Huber, P. & Koch, P. (2001). Value creation in the insurance industry. Risk Management and Insurance Review 4(2), 1–9.
   Google Scholar
• Henrion, R. (2006). Some remarks on value-at-risk optimization. International Journal of Management Science and Engineering Management 1(2), 111–118.
   Google Scholar
• Henrion, R. & Outrata, J. (2005). Calmness of constraint systems with applications. Mathematical Programming 104(2), 437–464.
   Web of Science ®Google Scholar
• Hörig, M. & Leitschkis, M. (2012). Solvency 2 proxy modelling via least squares Monte Carlo, Milliman Technical Report.
   Google Scholar
• Kaina, M. & Rüschendorf, L. (2009). On convex risk measures on ℒp spaces. Mathematical Methods of Operations Research 69(3), 475–495.
   Web of Science ®Google Scholar
• Kalberer, T. & Strkalj, Z. (2012). Is life really difficult? Milliman Research Reports.
   Google Scholar
• Koursaris, A. (2011). Calculating the solvency capital requirement. Insurance ERM. http://www.barrhibb.com/documents/downloads/CalculatingtheSolvencyCapitalRequirement-1-2.pdf
   Google Scholar
• Longstaff, F. & Schwartz, E. (2001). Valuing American options by simulation: a simple least-squares approach. The Review of Financial Studies 14(1), 113–147.
   Web of Science ®Google Scholar
• Natolski, J. & Werner, R. (2014). Mathematical analysis of different approaches for replicating portfolios. European Actuarial Journal 4(2), 411–435.
   Google Scholar
• Natolski, J. & Werner, R. (2016). Replicating portfolios: ℒ1 versus ℒ2 optimization. In Doerner K., Ljubic I., Pflug G. & Tragler G. Operations research proceedings. Cham: Springer. P. 533–538.
   Google Scholar
• Natolski J. & Werner R. (2017). Mathematical analysis of replication by cash flow matching. Risks 5(1), 13.
   Web of Science ®Google Scholar
• Oechslin, J., Aubry, O., Aellig, M., Kappeli, A., Bronnimann, D., Tandonnet, A. & Valois, G. (2007). Replicating embedded options. Life & Pensions Risk, February, 47–52.
   Google Scholar
• Pelsser, A. & Schweizer, J. (2016). The difference between LSMC and replicating portfolio in insurance liability modeling. European Actuarial Journal 6(2), 441–494.
   PubMed Web of Science ®Google Scholar
• Rockafellar, R. & Uryasev, S. (2002). Conditional value-at-risk for general loss distributions. Journal of Banking and Finance 26(7), 1443–1471.
   Web of Science ®Google Scholar
• Seemann A. (2011). Replizierende Portfolios in der deutschen Lebensversicherung. Ulm: ifa.
   Google Scholar
• Stentoft, L. (2001). Convergence of the least squares Monte Carlo approach to American option valuation. Management Science 50(9), 1193–1203.
   Web of Science ®Google Scholar
• Tsitsiklis, J. & van Roy, B. (2001). Regression methods for pricing complex American-style options. IEEE Transactions on Neural Networks 12(4), 694–703.
   PubMed Web of Science ®Google Scholar