Approximated Snell envelope and its applications

• Autorzy: Habibi Reza
• Języki publikacji: EN

Abstrakty

EN

This paper proposes some mild conditions on underlying stochastic process of optimal stopping and some approximations are proposed for Snell envelope techniques. The aim is to simplify the computation of conditional expectations which are necessary in obtaining the sequential backward Snell auxiliary process. Then, by applying these approximations to return process of a financial asset, the behaviors of optimal stopping times at which the expectation of return process is optimized are studied. Here, it is assumed that the mean corrected return process is of GARCH type.

Słowa kluczowe

EN

applied probability; GARCH; return process; Snell envelope

PL

zastosowane prawdopodobieństwo; GARCH; proces zwrotu; koperta Snella

• Wydawca: Wydawnictwo Politechniki Śląskiej
• Czasopismo: Silesian Journal of Pure and Applied Mathematics
• Rocznik: 2023
• Tom: Vol. 13, iss. 1
• Strony: 1--9
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Habibi Reza

• Iran Banking Institute, Central Bank of Iran, Tehran, Iran

Bibliografia

• 1. Ferguson T.S.: Optimal stopping and applications. Publisher: UCLA Mathematics Department, USA, 2007.
• 2. Lehmann El.L.: Elements of large-sample theory. Springer, USA, 2018.
• 3. Longstaff F.A., Schwartz E.S.: Valuing American options by simulation: a simple least square approach. Review of Financial approach, 14, 2001, 133-148.
• 4. Lustri C.J., Sofronov G.Y., Entwistle H.N.: On asymptotic of optimal stopping times. Technical report, Department of Mathematics and Statistics, Macquarie University, Australia, 2020.
• 5. Mai J.F., Scherer M.: Simulating copulas: stochastic models, sampling algorithms, and applications. Imperial College Press, UK, 2012.
• 6. Marti K.: Dynamic stochastic optimization. Springer, USA, 2004.
• 7. Peskir G., Shiryaev A.: Optimal stopping and free boundary problems. Birkhauser, Berlin, 2006.
• 8. Suli E., Mayers D.: An introduction to numerical analysis. Cambridge University Press, UK, 2003.
• 9. Wang D.: Generalized optimal stopping problems and financial markets. Longman Press, USA, 2010.