On perpetual American options in a multidimensional Black–Scholes model

References

• G. Alberti and L. Ambrosio, A geometrical approach to monotone functions in Rn, Math. Z. 230 (1999), pp. 259–316.
   Web of Science ®Google Scholar
• P. Briand, B. Delyon, Y. Hu, Y. E. Pardoux and L. Stoica, Lp solutions of backward stochastic differential equations, Stochastic Process. Appl. 108 (2003), pp. 109–129.
   Web of Science ®Google Scholar
• M. Broadie and J. Detemple, The valuation of American options on multiply assets, Math. Finance 7 (1997), pp. 241–286.
   Web of Science ®Google Scholar
• R.W.R. Darling and E. Pardoux, Backwards SDE with random terminal time and applications to semilinear elliptic PDE, Ann. Probab. 25 (1997), pp. 1135–1159.
   Web of Science ®Google Scholar
• C. Dellacherie and P.A. Meyer, Probabilities and Potential B. Theory of Martingales, North-Holland Publishing Co., Amsterdam. 1982.
   Google Scholar
• L.C. Evans, Partial Differential Equations, American Mathematical Society, Providence, RI. 1998.
   Google Scholar
• N. El Karoui, C. Kapoudjian, E. Pardoux, S. Peng and M.C. Quenez, Reflected solutions of backward SDEs, and related obstacle problems for PDE's, Ann. Probab. 25 (1997), pp. 702–737.
   Web of Science ®Google Scholar
• N. El Karoui, E. Pardoux and M.C. Quenez, Reflected backward SDEs and American options, Numerical methods in finance, Publ. Newton Inst., 13, Cambridge University Press, Cambridge, 1997, pp. 215–231.
   Google Scholar
• N. El Karoui and M.C. Quenez, Non-linear Pricing Theory and Backward Stochastic Differential Equations, (Lecture Notes in Math. vol. 1656).Berlin, Springer, 1997.
   Google Scholar
• M. Fuhrman and G. Tessitore, Infinite horizon backward stochastic differential equations and elliptic equations in hilbert spaces, Ann. Probab. 32 (1B) (2004), pp. 607–660.
   Web of Science ®Google Scholar
• S. Hamadène, J.-P. Lepeltier and Z. Wu, Infinite horizon reflected backward stochastic differential equations and applications in mixed control and game problems, Probab. Math. Statist 19(2) (1999), pp. 211–234.
   Google Scholar
• S. Jacka, Optimal stopping and the American put, Math. Finance 1(2) (1991), pp. 1–14.
   Google Scholar
• I. Karatzas, On the pricing of American options, Appl. Math. Optim. 17 (1988), pp. 37–60.
   Web of Science ®Google Scholar
• I. Karatzas and S.E. Shreve, Methods of Mathematical Finance, Springer, New York, 1998.
   Google Scholar
• T. Klimsiak, Quasi-regular Dirichlet forms and the obstacle problem for elliptic equations with measure data, Studia Math. 258 (2021), pp. 121–156.
   Web of Science ®Google Scholar
• T. Klimsiak and A. Rozkosz, On backward stochastic differential equations approach to valuation of American options, Bull. Polish Acad. Sci. Math. 59 (2011), pp. 275–288.
   Google Scholar
• T. Klimsiak and A. Rozkosz, The early exercise premium representation for American options on multiply assets, Appl. Math. Optim. 73 (2016), pp. 99–114.
   Web of Science ®Google Scholar
• T. Klimsiak and A. Rozkosz, The valuation of American options in a multidimensional exponential Lévy model, Math. Finance. 28 (2018), pp. 1107–1142.
   Web of Science ®Google Scholar
• T. Klimsiak and A. Rozkosz, Large time behaviour of solutions to parabolic equations with Dirichlet operators and nonlinear dependence on measure data, Potential Anal. 51 (2019), pp. 255–289.
   Web of Science ®Google Scholar
• N.V. Krylov, Controlled Diffusion Processes, Springer, New York, 1980.
   Google Scholar
• H.P. McKean Jr., A free-boundary problem for the heat equation arising from a problem in mathematical economics, Industr. Manag. Rev. 6 (1965), pp. 32–39.
   Google Scholar
• R.C. Merton, Theory of rational option pricing, Bell J. Econom. Manage. Sci. 4 (1973), pp. 141–183.
   Web of Science ®Google Scholar
• P. Protter, Stochastic Integration and Differential Equations, Second Ed., Springer, Berlin, 2004.
   Google Scholar
• A. Rozkosz and L. Słomiński, Stochastic representation of entropy solutions of semilinear elliptic obstacle problems with measure data, Electron. J. Probab. 17(40) (2012), pp. 1–27.
   Google Scholar
• S.E. Shreve, Stochastic Calculus for Finance II. Continuous-Time Models, Springer, New York, 2004.
   Google Scholar