| 1. |
- Arnarson, Teitur, et al.
(author)
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A PDE approach to regularity of solutions to finite horizon optimal switching problems
- 2009
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In: Nonlinear Analysis. - : Elsevier BV. - 0362-546X .- 1873-5215. ; 71:12, s. 6054-6067
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Journal article (peer-reviewed)abstract
- We study optimal 2-switching and n-switching problems and the corresponding system of variational inequalities. We obtain results on the existence of viscosity solutions for the 2-switching problem for various setups when the cost of switching is non-deterministic. For the n-switching problem we obtain regularity results for the solutions of the variational inequalities. The solutions are C-l,C-l-regular away for the free boundaries of the action sets.
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| 2. |
- Arnarson, Teitur
(author)
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Early exercise boundary regularity close to expiry in the indifference setting : A PDE approach
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Journal article (other academic/artistic)abstract
- The free boundary problem that occurs when pricing American options is studied in a general setting. We investigate the regularity of the free boundary close to initial state using the so called blow-up technique. This problem has been studied extensively and good results are known for the linear, one-dimensional case. The blow-up technique, however, works also for non-linear PDE in higher dimensions. For illustration we apply the technique to the indierence pricing model where the involved PDE is non-linear.
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| 3. |
- Arnarson, Teitur, et al.
(author)
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On the size of the non-coincidence set of parabolic obstacle problems with applications to American option pricing
- 2007
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In: Mathematica Scandinavica. - : Det Kgl. Bibliotek/Royal Danish Library. - 0025-5521 .- 1903-1807. ; 101:1, s. 148-160
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Journal article (peer-reviewed)abstract
- The following paper is devoted to the study of the positivity set U = {L phi > 0} arising in parabolic obstacle problems. It is shown that U is contained in the non-coincidence set with a positive distance between the boundaries uniformly in the spatial variable if the boundary of U satisfies an interior C-1 -Dini condition in the space variable and a Lipschitz condition in the time variable. We apply our results to American option pricing and we thus show that the positivity set is strictly contained in the continuation region, which means that the option should not be exercised in U or on the boundary of U.
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| 4. |
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| 5. |
- Arnarson, Teitur, 1977-
(author)
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PDE methods for free boundary problems in financial mathematics
- 2008
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Doctoral thesis (other academic/artistic)abstract
- We consider different aspects of free boundary problems that have financial applications. Papers I–III deal with American option pricing, in which case the boundary is called the early exercise boundary and separates the region where to hold the option from the region where to exercise it. In Papers I–II we obtain boundary regularity results by local analysis of the PDEs involved and in Paper III we perform local analysis of the corresponding stochastic representation. The last paper is different in its character as we are dealing with an optimal switching problem, where a switching of state occurs when the underlying process crosses a free boundary. Here we obtain existence and regularity results of the viscosity solutions to the involved system of variational inequalities.
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| 6. |
- Arnarson, Teitur
(author)
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The blow-up technique in terms of stochastics applied to optimal stopping problems in finance
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Other publication (other academic/artistic)abstract
- The blow-up technique is a useful tool for local analysis in PDEtheory. It is applicable to non-linear, higher dimensional PDEs. In this paperwe translate the blow-up technique to stochastic terms by considering thestochastic representation of solutions to PDEs. For illustration we apply theblow-up technique to obtain the early exercise boundary regularity close to expiryfor American put and call options in the classic Black-Scholes framework.
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