Optimal stopping problems in diffusion-type models with running maxima and drawdowns
| Autor: | Neofytos Rodosthenous, Pavel V. Gapeev |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Statistics and Probability
Mathematical optimization General Mathematics Markov process 01 natural sciences symbols.namesake 010104 statistics & probability running maximum and running maximum drawdown process 34K10 Stopping time normal reflection FOS: Mathematics Free boundary problem Optimal stopping Multidimensional optimal stopping problem 0101 mathematics 60G40 Brownian motion 60J60 Mathematics 60G40 34K10 91B70 60J60 34L30 91B25 change-of-variable formula with local time on surfaces Probability (math.PR) 010102 general mathematics instantaneous stopping and smooth fit 34L30 91B25 91B70 perpetual American option symbols Dividend free-boundary problem Volatility (finance) Statistics Probability and Uncertainty Maxima Mathematics - Probability |
| Zdroj: | J. Appl. Probab. 51, no. 3 (2014), 799-817 |
| Popis: | We study optimal stopping problems related to the pricing of perpetual American options in an extension of the Black-Merton-Scholes model in which the dividend and volatility rates of the underlying risky asset depend on the running values of its maximum and maximum drawdown. The optimal stopping times of the exercise are shown to be the first times at which the price of the underlying asset exits some regions restricted by certain boundaries depending on the running values of the associated maximum and maximum drawdown processes. We obtain closed-form solutions to the equivalent free-boundary problems for the value functions with smooth fit at the optimal stopping boundaries and normal reflection at the edges of the state space of the resulting three-dimensional Markov process. We derive first-order nonlinear ordinary differential equations for the optimal exercise boundaries of the perpetual American standard options. |
| Databáze: | OpenAIRE |
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