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On a general class of free boundary problems for European-style installment options with continuous payment plan
1. | Department of Economics, Faculty of Economics "Federico Caffè", University of Rome III, Via Silvio D'Amico 77, 00145 Rome, Italy |
References:
[1] |
G. Alobaidi, R. Mallier and A. S. Deakin, Laplace transforms and installment options, Mathematical Models and Methods in Applied Sciences, 14 (2004), 1167-1189.
doi: 10.1142/S0218202504003581. |
[2] |
G. Alobaidi and R. Mallier, Installment options close to expiry, Journal of Applied Mathematics and Stochastic Analysis, (2006), Art. ID 60824, 1-9.
doi: 10.1155/JAMSA/2006/60824. |
[3] |
H. Ben-Ameur, M. Breton and P. François, A dynamic programming approach to price installment options, European Journal of Operational Research, 169 (2006), 667-676.
doi: 10.1016/j.ejor.2004.05.009. |
[4] |
P. Carr, R. Jarrow and R. Myneni, Alternative characterizations of American put options, Mathematical Finance, 2 (1992), 87-106.
doi: 10.1111/j.1467-9965.1992.tb00040.x. |
[5] |
P. Ciurlia, On the evaluation of European continuous-installment options, Department of Economics Working paper, No 113 (2010), University of Rome III. |
[6] |
P. Ciurlia and C. Caperdoni, A note on the pricing of perpetual continuous-installment options, Mathematical Methods in Economics and Finance, 4 (2009), 11-26. |
[7] |
P. Ciurlia and I. Roko, Valuation of American continuous-installment options, Computational Economics, 25 (2005), 143-165.
doi: 10.1007/s10614-005-6279-4. |
[8] |
M. Davis, W. Schachermayer and R. Tompkins, Pricing, no-arbitrage bounds and robust hedging of instalment options, Quantitative Finance, 1 (2001), 597-610.
doi: 10.1088/1469-7688/1/6/302. |
[9] |
M. Davis, W. Schachermayer and R. Tompkins, Installment options and static hedging, Journal of Risk Finance, 3 (2002), 46-52.
doi: 10.1108/eb043487. |
[10] |
S. Griebsch, C. Kühn and U. Wystup, Instalment options: A closed-form solution and the limiting case, in "Mathematical Control Theory and Finance" (eds. A. Sarychev, A. Shiryaev, M. Guerra and M.d.R. Grossinho), Springer-Verlag, Berlin, (2008), 211-229.
doi: 10.1007/978-3-540-69532-5_12. |
[11] |
S. D. Jacka, Optimal stopping and the American put, Mathematical Finance, 1 (1991), 1-14.
doi: 10.1111/j.1467-9965.1991.tb00007.x. |
[12] |
F. Karsenty and J. Sikorav, Installment plan, Risk, 6 (1993), 36-40. |
[13] |
I. J. Kim, The analytical valuation of American options, Review of Financial Studies, 3 (1990), 547-572.
doi: 10.1093/rfs/3.4.547. |
[14] |
T. Kimura, American continuous-installment options: valuation and premium decomposition, SIAM Journal on Applied Mathematics, 70 (2009), 803-824.
doi: 10.1137/080740969. |
[15] |
T. Kimura, Valuing continuous-installment options, European Journal of Operational Research, 201 (2010), 222-230.
doi: 10.1016/j.ejor.2009.02.010. |
[16] |
H. P. McKean, Appendix: A free boundary problem for the heat equation arising from a problem in mathematical economics, Industrial Management Review, 6 (1965), 32-39. |
[17] |
Z. Yang and F. Yi, A variational inequality arising from American installment call options pricing, Journal of Mathematical Analysis and Applications, 357 (2009), 54-68.
doi: 10.1016/j.jmaa.2009.03.045. |
[18] |
F. Yi, Z. Yang and X. Wang, A variational inequality arising from European installment call options pricing, SIAM Journal on Mathematical Analysis, 40 (2008), 306-326.
doi: 10.1137/060670353. |
show all references
References:
[1] |
G. Alobaidi, R. Mallier and A. S. Deakin, Laplace transforms and installment options, Mathematical Models and Methods in Applied Sciences, 14 (2004), 1167-1189.
doi: 10.1142/S0218202504003581. |
[2] |
G. Alobaidi and R. Mallier, Installment options close to expiry, Journal of Applied Mathematics and Stochastic Analysis, (2006), Art. ID 60824, 1-9.
doi: 10.1155/JAMSA/2006/60824. |
[3] |
H. Ben-Ameur, M. Breton and P. François, A dynamic programming approach to price installment options, European Journal of Operational Research, 169 (2006), 667-676.
doi: 10.1016/j.ejor.2004.05.009. |
[4] |
P. Carr, R. Jarrow and R. Myneni, Alternative characterizations of American put options, Mathematical Finance, 2 (1992), 87-106.
doi: 10.1111/j.1467-9965.1992.tb00040.x. |
[5] |
P. Ciurlia, On the evaluation of European continuous-installment options, Department of Economics Working paper, No 113 (2010), University of Rome III. |
[6] |
P. Ciurlia and C. Caperdoni, A note on the pricing of perpetual continuous-installment options, Mathematical Methods in Economics and Finance, 4 (2009), 11-26. |
[7] |
P. Ciurlia and I. Roko, Valuation of American continuous-installment options, Computational Economics, 25 (2005), 143-165.
doi: 10.1007/s10614-005-6279-4. |
[8] |
M. Davis, W. Schachermayer and R. Tompkins, Pricing, no-arbitrage bounds and robust hedging of instalment options, Quantitative Finance, 1 (2001), 597-610.
doi: 10.1088/1469-7688/1/6/302. |
[9] |
M. Davis, W. Schachermayer and R. Tompkins, Installment options and static hedging, Journal of Risk Finance, 3 (2002), 46-52.
doi: 10.1108/eb043487. |
[10] |
S. Griebsch, C. Kühn and U. Wystup, Instalment options: A closed-form solution and the limiting case, in "Mathematical Control Theory and Finance" (eds. A. Sarychev, A. Shiryaev, M. Guerra and M.d.R. Grossinho), Springer-Verlag, Berlin, (2008), 211-229.
doi: 10.1007/978-3-540-69532-5_12. |
[11] |
S. D. Jacka, Optimal stopping and the American put, Mathematical Finance, 1 (1991), 1-14.
doi: 10.1111/j.1467-9965.1991.tb00007.x. |
[12] |
F. Karsenty and J. Sikorav, Installment plan, Risk, 6 (1993), 36-40. |
[13] |
I. J. Kim, The analytical valuation of American options, Review of Financial Studies, 3 (1990), 547-572.
doi: 10.1093/rfs/3.4.547. |
[14] |
T. Kimura, American continuous-installment options: valuation and premium decomposition, SIAM Journal on Applied Mathematics, 70 (2009), 803-824.
doi: 10.1137/080740969. |
[15] |
T. Kimura, Valuing continuous-installment options, European Journal of Operational Research, 201 (2010), 222-230.
doi: 10.1016/j.ejor.2009.02.010. |
[16] |
H. P. McKean, Appendix: A free boundary problem for the heat equation arising from a problem in mathematical economics, Industrial Management Review, 6 (1965), 32-39. |
[17] |
Z. Yang and F. Yi, A variational inequality arising from American installment call options pricing, Journal of Mathematical Analysis and Applications, 357 (2009), 54-68.
doi: 10.1016/j.jmaa.2009.03.045. |
[18] |
F. Yi, Z. Yang and X. Wang, A variational inequality arising from European installment call options pricing, SIAM Journal on Mathematical Analysis, 40 (2008), 306-326.
doi: 10.1137/060670353. |
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