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http://dx.doi.org/10.5666/KMJ.2022.62.4.615

Time-dependent Double Obstacle Problem Arising from European Option Pricing with Transaction Costs  

Jehan, Oh (Department of Mathematics, Kyungpook National University)
Namgwang, Woo (Department of Mathematics, Kyungpook National University)
Publication Information
Kyungpook Mathematical Journal / v.62, no.4, 2022 , pp. 615-640 More about this Journal
Abstract
In this paper, we investigate a time-dependent double obstacle problem associated with the model of European call option pricing with transaction costs. We prove the existence and uniqueness of a W2,1p,loc solution to the problem. We then characterize the behavior of the free boundaries in terms of continuity and values of limit points.
Keywords
double obstacle problem; parabolic partial differential equation; time-dependent obstacle; free boundary; option pricing;
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  • Reference
1 M. Akian, J. L. Menaldi and A. Sulem, On an investment-consumption model with transaction costs, SIAM J. Control Optim., 34(1)(1996), 329-364.    DOI
2 X. Chen, Y. Chen and F. Yi, Parabolic variational inequality with parameter and gradient constraints, J. Math. Anal. Appl., 385(2)(2012), 928-946.    DOI
3 M. Dai and F. Yi, Finite-horizon optimal investment with transaction costs: a parabolic double obstacle problem, J. Differential Equations, 246(4)(2009), 1445-1469.    DOI
4 M. H. A. Davis, V. G. Panas and T. Zariphopoulou, European option pricing with transaction costs, SIAM J. Control Optim., 31(2)(1993), 470-493.    DOI
5 A. Friedman, Parabolic variational inequalities in one space dimension and smoothness of the free boundary, J. Functional Analysis, 18(1975), 151-176.    DOI
6 P. Guasoni, Optimal investment with transaction costs and without semimartingales, Ann. Appl. Probab., 12(4)(2002), 1227-1246.    DOI
7 G. M. Lieberman, Second order parabolic differential equations, World Scientific Publishing Co.,Inc., River Edge, NJ, 1996. 
8 OECD: Organisation for Economic Co-Operation and Development, OECD Economic Outlook, Organization for Economic Co-operation and Development (OECD), Paris Cedex, France, 81 edition, July 2007. 
9 O. A. Oleinik and E. V. Radkevic, Second order equations with nonnegative characteristic form, Translated from the Russian by Paul C. Fife. Plenum Press, New York-London, 1973. 
10 R. Pollin, D. Baker and M. Schaberg, Securities transaction taxes for US financial markets, Eastern Economic Journal, 29(4)(2003), 527-558. 
11 K. Tso, On an Aleksandrov-Bakel'man type maximum principle for second-order parabolic equations, Comm. Partial Differential Equations, 10(5)(1985), 543-553.    DOI
12 Z. Yang and F. Yi, Valuation of European installment put option: variational inequality approach, Commun. Contemp. Math., 11(2)(2009), 279-307.    DOI
13 F. Yi and Z. Yang, A variational inequality arising from European option pricing with transaction costs, Sci. China Ser. A, 51(5)(2008), 935-954.   DOI