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On RVaR-based optimal partial hedging

Published online by Cambridge University Press:  25 January 2022

Alexander Melnikov  and
Hongxi Wan Open the ORCID record for Hongxi Wan [Opens in a new window]
Alexander Melnikov
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
Hongxi Wan*
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
*
*Corresponding author. E-mail: hongxi@ualberta.ca
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Abstract

The main aim of this paper is to develop an optimal partial hedging strategy that minimises an investor’s shortfall subject to an initial wealth constraint. The risk criterion we employ is a robust tail risk measure called Range Value-at-Risk (RVaR) which belongs to a wider class of distortion risk measures and contains the well-known measures VaR and CVaR as important limiting cases. Explicit forms of such RVaR-based optimal hedging strategies are derived. In addition, we provide a numerical example to demonstrate how to apply this more comprehensive methodology of partial hedging in the area of mixed finance/insurance contracts in the market with long-range dependence.

Keywords

Partial hedgingRange Value-at-RiskMixed Fractional Brownian motionEquity-linked life insurance contracts
Type
Original Research Paper
Information
Annals of Actuarial Science , Volume 16 , Issue 2 , July 2022 , pp. 349 - 366
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

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References

Artzner, P., Delbaen, F., Eber, J.M. & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9(3), 203–228.CrossRefGoogle Scholar
Belles-Sampera, J., Guillén, M. & Santolino, M. (2014). Beyond value-at-risk: GlueVaR distortion risk measures. Risk Analysis, 34(1), 121–134.CrossRefGoogle ScholarPubMed
Bernard, C., Moraux, F., Rüschendorf, L. & Vanduffel, S. (2015). Optimal payoffs under state-dependent preferences. Quantitative Finance, 15(7), 1157–1173.CrossRefGoogle Scholar
Bratyk, M. & Mishura, Y. (2008). The generalization of the quantile hedging problem for price process model involving finite number of Brownian and Fractional Brownian motions. Theory of Stochastic Processes, 14, 27–38.Google Scholar
Brennan, M. & Schwartz, E.S. (1976). The pricing of equity-linked life insurance policies with an asset value guarantee. Journal of Financial Economics, 3(3), 195–213.CrossRefGoogle Scholar
Cheridito, P. (2001). Mixed fractional Brownian motion. Bernoulli, 7(6), 913–934.CrossRefGoogle Scholar
Cong, J., Tan, K.S. & Weng, C. (2013). VaR-based optimal partial hedging. ASTIN Bulletin, 43(3), 271–299.CrossRefGoogle Scholar
Cong, J., Tan, K.S. & Weng, C. (2014). CVaR-based optimal partial hedging. The Journal of Risk, 16(3), 49–83.CrossRefGoogle Scholar
Cont, R., Deguest, R. & Scandolo, G. (2010). Robustness and sensitivity analysis of risk measurement procedures. Quantitative Finance, 10(6), 593–606.CrossRefGoogle Scholar
Dhaene, J., Denuit, M., Goovaerts, M.J., Kaas, R. & Vyncke, D. (2002). The concept of comonotonicity in actuarial science and finance: theory. Insurance: Mathematics and Economics, 31(1), 3–33.Google Scholar
Embrechts, P., Liu, H. & Wang, R. (2018). Quantile-based risk sharing. Operations Research, 66(4), 936–949.CrossRefGoogle Scholar
Föllmer, H. & Leukert, P. (1999). Quantile hedging. Finance and Stochastics, 3(3), 251–273.CrossRefGoogle Scholar
Föllmer, H. & Leukert, P. (2000). Efficient hedging: cost versus shortfall risk. Finance and Stochastics, 4(2), 117–146.Google Scholar
Henderson, V. & Hobson, D. (2004). Utility indifference pricing: an overview. In Indifference Pricing: Theory and Applications. Princeton University Press.Google Scholar
Kirch, M. & Melnikov, A. (2005). Efficient hedging and pricing of life insurance policies in a Jump-Diffusion model. Stochastic Analysis and Applications, 23(6), 1213–1233.CrossRefGoogle Scholar
Madan, D. & Schoutens, W. (2016). Applied Conic Finance. Cambridge University Press.CrossRefGoogle Scholar
Melnikov, A. & Mishura, Y. (2011). On pricing and hedging in financial markets with long-range dependence. Mathematics and Financial Economics, 5, 29–46.CrossRefGoogle Scholar
Melnikov, A. & Nosrati, A. (2017). Equity-Linked Life Insurance Partial Hedging Methods. ImprintChapman and Hall/CRC.Google Scholar
Melnikov, A. & Romanyuk, Y. (2008). Efficient hedging and pricing of equitylinked life insurance contracts on several risky assets. International Journal of Theoretical and Applied Finance, 11(3), 295–323.CrossRefGoogle Scholar
Melnikov, A. & Smirnov, I. (2012). Dynamic hedging of conditional value-atrisk. Insurance: Mathematics and Economics, 51(1), 182–190.Google Scholar
Melnikov, A. & Skornyakova, V. (2005). Quantile hedging and its application to life insurance. Statistics and Decisions, 23(4), 301–316.CrossRefGoogle Scholar
Nakano, Y. (2011). Partial hedging for defaultable claims. In S. Kusuoka & T. Maruyama (Eds.), Advances in Mathematical Economics (pp. 127–145).CrossRefGoogle Scholar
Rolski, T., Schmidli, H., Schmidt, V. & Teugels, J.L. (1999). Stochastic Processes for Insurance and Finance, vol. 6. John Wiley & Sons.CrossRefGoogle Scholar
Spivak, G. & Cvitanić, J. (1999). Maximizing the probability of a perfect hedge. The Annals of Applied Probability, 9(4), 1303–1328.Google Scholar
Xu, M. (2006). Risk measure pricing and hedging in incomplete markets. Annals of Finance, 2, 57–71.CrossRefGoogle Scholar