427
Views
15
CrossRef citations to date
0
Altmetric
Research Article

Optimal investment and reinsurance strategies under 4/2 stochastic volatility model

ORCID Icon, , &
Pages 413-449 | Received 26 Sep 2021, Accepted 28 Jul 2022, Published online: 31 Aug 2022

References

  • Abramowitz, M. & Stegun, I. (1972). Handbook of mathematical functions with formulas, graphs and mathematical tables. New York: Dover.
  • Bally, V. & Kohatsu-Higa, A. (2015). A probabilistic interpretation of the parametrix method. Annals of Applied Probability 25(6), 3095–3138.
  • Bluman, G., Cheviakov, A. & Anco, S. (2010). Applications of symmetry methods to partial differential equations. Applied Mathematical Sciences, 168, New York: Springer-Verlag.
  • Boguslavskaya, E. & Muravey, D. (2015). An explicit solution for optimal investment in Heston model. Theory of Probability and Its Applications 60(4), 811–819.
  • Borodin, A. & Salminen, P. (2002). Handbook of brownian motion – facts and formulae, 2nd ed. Basel: Birkhauser.
  • Cheng, Y. & Escobar-Anel, M. (2021). Optimal investment strategy in the family of 4/2 stochastic volatility models. Quantitative Finance 21(10), 1723–1751.
  • Corielli, F., Foschi, P. & Pascucci, A. (2010). Parametrix approximation of diffusion transition densities. SIAM Journal on Financial Mathematics 1, 833–867.
  • Craddock, M. (2009). Fundamental solutions, transition densities and the integration of Lie symmetries. Journal of Differential Equations 246(6), 2538–2560.
  • Craddock, M. & Lennox, K. (2009). The calculation of expectations for classes of diffusion processes by Lie symmetry methods. Annals of Applied Probability 19(1), 127–157.
  • Craddock, M. & Platen, E. (2009). On explicit probability laws for classes of scalar diffusions. Research Paper Series, 246.
  • Da Fonseca, J. & Grasselli, M. (2011). Riding on the smiles. Quantitative Finance 11(11), 1609–1632.
  • Deck, T. & Kruse, S. (2002). Parabolic differential equations with unbounded coefficients–a generalization of the parametrix method. Acta Applicandae Mathematicae 74, 71–91.
  • Dorodnitsyn, V. (2011). Applications of Lie groups to difference equations. Differential and Integral Equations and Their Applications, 8, Boca Raton: CRC Press.
  • Friedman, A. (1983). Partial differential equations of parabolic type. Florida: Robert E. Krieger.
  • Grasselli, M. (2017). The 4/2 stochastic volatility model: a unified approach for the Heston and the 3/2 model. Mathematical Finance 27(4), 1013–1034.
  • Hata, H. & Yasuda, K. (2018). Expected exponential utility maximization of insurers with a linear Gaussian stochastic factor model. Scandinavian Actuarial Journal 2018(5), 357–378.
  • Heston, S. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies 6, 327–343.
  • Heston, S. (1997). A simple new formula for options with stochastic volatility. Technical Report, Washington University of St. Louis.
  • Itkin, A. (2013). New solvable stochastic volatility models for pricing volatility derivatives. Review of Derivatives Research 16, 111–134.
  • Kraft, H. (2005). Optimal portfolios and Heston's stochastic volatility model: an explicit solution for power utility. Quantative Finance 5(3), 303–313.
  • Levi, E. (1907). Sulle equazioni lineari totalmente ellittiche alle derivate parziali. Rendiconti Del Circolo Matematico Di Palermo 24, 275–317.
  • Li, Z., Zeng, Y. & Lai, Y. (2012). Optimal time-consistent investment and reinsurance strategies for insurers under Heston's SV model. Insurance: Mathematics and Economics 51, 191–203.
  • Lin, X. & Qian, Y. (2016). Time-consistent mean-variance reinsurance-investment strategy for insurers under CEV model. Scandinavian Actuarial Journal 2016(7), 646–671.
  • Liu, J., Yiu, K. & Siu, T. (2014). Optimal investment of an insurer with regime-switching and risk constraint. Scandinavian Actuarial Journal 2014(7), 583–601.
  • Liu, J., Yiu, K., Siu, T. & Ching, W. (2013). Optimal investment-reinsurance with dynamic risk constraint and regime switching. Scandinavian Actuarial Journal 2013(4), 263–285.
  • Luenberger, D. (1968). Optimization by vector space methods. New York: John Wiley.
  • Muravey, D. (2020). Lie symmetries methods in boundary crossing problems for diffusion processes. Acta Applicandae Mathematicae 170(1), 347–372.
  • Olver, P. (1993). Applications of Lie groups to differential equations. 2nd ed., Graduate Texts in Mathematics, 107, New York: Springer.
  • Pascucci, A. & Pesce, A. (2020). The parametrix method for parabolic SPDEs. Stochastic Processes and Their Applications 130(10), 6226–6245.
  • Platen, E. (1997). A non-linear stochastic volatility model. Financial Mathematical Research Report No. FMRR005-97, Center of Financial Mathematics, Australian National University.
  • Protter, P. (2004). Stochastic integration and differential equations. 2nd ed. Berlin Heidelberg, New York: Springer.
  • Pun, C. & Wong, H. (2015). Robust investment-reinsurance optimization with multiscale stochastic volatility. Insurance: Mathematics and Economics 62, 245–256.
  • Razborova, P., Kara, A. & Biswas, A. (2015). Additional conservation laws for Rosenau-KdV-RLW equation with power law nonlinearity by Lie symmetry. Nonlinear Dynamics 79, 743–748.
  • Shen, Y. & Zeng, Y. (2015). Optimal investment-reinsurance strategy for mean-variance insurers with square-root factor process. Insurance: Mathmatics and Economics 62, 118–137.
  • Sun, Z., Zhang, X. & Yuen, K. (2020). Mean-variance asset-liability management with affine diffusion factor process and a reinsurance option. Scandinavian Actuarial Journal 2020(3), 218–244.
  • Swiss Re Institute (2020). Lower for even longer: what does the low interest rate economy mean for insurers? Economic and Insurance Outlook Report (Authors: Fan, I., Holzheu, T., Kubli, D., Saner, P.). Available at: https://www.swissre.com/institute/research/topics-and-risk-dialogues/economy-and-insurance-outlook/expertise-publication-low-interest-rates.html.
  • Wiggins, J. (1987). Option values under stochastic volatility: theory and empirical estimates. Journal of Financial Economics 19(2), 351–372.
  • Yan, T. & Wong, H. (2020). Open-loop equilibrium reinsurance-investment strategy under mean-variance criterion with stochastic volatility. Insurance: Mathematics and Economics 90, 105–119.
  • Zariphopoulou, T. (2001). A solution approach to valuation with unhedgeable risks. Finance and Stochastics 5(1), 61–82.
  • Zeng, X. & Taksar, M. (2013). A stochastic volatility model and optimal portfolio selection. Quantitative Finance 13(10), 1547–1558.
  • Zhao, H., Rong, X. & Zhao, Y. (2013). Optimal excess-of-loss reinsurance and investment problem for an insurer with jump-diffusion risk process under the Heston model. Insurance: Mathmatics and Economics 53, 504–514.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.