A numerical scheme for the impulse control formulation for pricing variable annuities with a guaranteed minimum withdrawal benefit (GMWB)

Numerische Mathematik

Volumn 109, Issue 4, 2008, Pages 535-569

  Chen, Zhuliang ^a   Forsyth, Peter A ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 44649103222     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-008-0152-z     Document Type: Article

References (22)

1. Amadori A.L.: Quasi-variational inequalities with Dirichlet boundary condition related to exit time problems for impulse control. SIAM J. Control Optim. 43(2), 570-589 (2004)
2. Barles G.: Convergence of numerical schemes for degenerate parabolic equations arising in finance. In: Rogers, L.C.G., Talay, D.(eds) Numerical Methods in Finance, pp. 1-21. Cambridge University Press, Cambridge (1997)
3. Barles G., Souganidis P.E.: Convergence of approximation schemes for fully nonlinear equations. Asymptotic Anal. 4, 271-283 (1991)
4. Bauer, D., Kling, A., Russ, J.: A universal pricing framework for guaranteed minimum benefits in variable annuities. Working paper, Ulm University
5. Chen, Z., Forsyth, P.A.: A numerical scheme for the impulse control formulation for pricing variable annuities with a guaranteed minimum withdrawal benefit (GMWB). Technical report, University of Waterloo, July 2007
6. Chen Z., Forsyth P.A.: A semi-Lagrangian approach for natural gas storage valuation and optimal operation. SIAM J. Sci. Comput. 30(1), 339-368 (2007)
7. Cont R., Tankov P.: Financial Modelling with Jump Processes. Chapman and Hall, London (2004)
8. Dai, M., Kwok, Y.K., Zong, J.: Guaranteed minimum withdrawal benefit in variable annuities. Math. Finance (2008, in press)
9. Davis M.H.A., Panas V.G., Zariphopoulou T.: European option pricing with transaction costs. SIAM J. Control Optim. 31(2), 470-493 (1993)
10. D'Halluin Y., Forsyth P.A., Labahn G.: A semi-Lagrangian approach for American Asian options under jump diffusion. SIAM J. Sci. Comput. 27(1), 315-345 (2005)
11. Forsyth, P.A., Labahn, G.: Numerical methods for controlled Hamilton-Jacobi-Bellman PDEs in finance. J. Comput. Finance 11:1-44, 2007/8(Winter)
12. Ishii K.: Viscosity solutions of nonlinear second order elliptic PDEs associated with impulse control problems II. Funkcialaj Ekvacioj 38, 297-328 (1995)
13. Korn R.: Some applications of impulse control in mathematical finance. Math. Methods Oper. Res. 50, 493-518 (1999)
14. Milevsky M.A., Salisbury T.S.: Financial valuation of guaranteed minimum withdrawal benefits. Insur. Math. Econ. 38, 21-38 (2006)
15. Øksendal B., Sulem A.: Optimal consumption and portfolio with both fixed and proportional transaction costs. SIAM J. Control Optim. 40(6), 1765-1790 (2002)
16. Pham H.: On some recent aspects of stochastic control and their applications. Probab. Surveys 2, 506-549 (2005)
17. Tourin A., Zariphopoulou T.: Numerical schemes for investment models with singular transactions. Comput. Econ. 7, 287-307 (1994)
18. Vath V.L., Mnif M., Pham H.: A model of optimal portfolio selection under liquidity risk and price impact. Finance Stochastics 11, 51-90 (2007)
19. Wilmott P.: Derivatives: The Theory and Practice of Financial Engineering. John Wiley & Sons, West Sussex (1998)
20. Windcliff H., Forsyth P.A., Le Roux M.K., Vetzal K.R.: Understanding the behaviour and hedging of segregated funds offering the reset feature. North Am. Actuarial J. 6, 107-125 (2002)
21. Windcliff H.A., Forsyth P.A., Vetzal K.R.: Valuation of segregated funds: shout options with maturity extensions. Insur Math. Econ. 29, 1-21 (2001)
22. Zakamouline V.I.: A unified approach to portfolio optimization with linear transaction costs. Math. Methods Oper. Res. 62, 319-343 (2005)