A new explicit solution is obtained for a general class of two-dimensional optimal stopping problems arising in real option theory. First, the solvable case of homogeneous and quasi-homogeneous problems is presented in a comprehensive framework. Then the general problem - including the unsolved case of inhomogeneous function - is considered and an explicit expression for the value function is obtained in terms of a modified Bessel function of second kind. Then we clarify the link between the general solution method and the more elementary one in the specific (quasi-)homogeneous problem. Finally, this article provides some useful formulas and some insights for the one-dimensional case as well.
A general framework for optimal stopping problems with two risk factors and real option applications / Rossella Agliardi. - In: APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY. - ISSN 1526-4025. - STAMPA. - 40:1(2023), pp. 161-179. [10.1002/asmb.2810]
A general framework for optimal stopping problems with two risk factors and real option applications
Rossella Agliardi
2023
Abstract
A new explicit solution is obtained for a general class of two-dimensional optimal stopping problems arising in real option theory. First, the solvable case of homogeneous and quasi-homogeneous problems is presented in a comprehensive framework. Then the general problem - including the unsolved case of inhomogeneous function - is considered and an explicit expression for the value function is obtained in terms of a modified Bessel function of second kind. Then we clarify the link between the general solution method and the more elementary one in the specific (quasi-)homogeneous problem. Finally, this article provides some useful formulas and some insights for the one-dimensional case as well.File | Dimensione | Formato | |
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