Abstract
In this chapter we introduce the “optimal growth strategy” and the associated “optimal growth portfolios” in markets of semimartingale models. We work out expressions of “optimal growth portfolios” in a geometric Lévy process model and a jump-diffusion-like process model. In Sect. 14.2, we present the “numeraire portfolio approach” to contingent claim pricing in a geometric Lévy process model. In Sect. 14.3 we give an overview of other martingale measure approaches to contingent claim pricing.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Bajeux-Besnainou, I., Portrait, R.: The numeraire portfolio: a new perspective on financial theory. Eur. J. Financ. 3, 291–309 (1997)
Bühlmann, H., Delbaen, F., Embrechts, P., Shiryaeve, A.N.: No-arbitrage, change of measure and conditional Esscher transforms. CWI Q. Amst. 9(4), 291–317 (1996)
Chan, T.: Pricing contingent claims on stocks driven by Lévy processes. Ann. Appl. Probab. 9(2), 504–528 (1999)
Davis, M.H.A.: Option pricing in incomplete markets. In: Dempster, A.H., Pliska, S.R. (eds.) Mathematics of Derivative Securities, pp. 216–226. Publications of the Newton Institute, Cambridge University Press, Cambridge (1997)
Föllmer, H., Schweizer, M.: Hedging of contingent claims under incomplete information. In: Davis, M.H.A., Elliott, R.J. (eds.) Applied Stochastic Analysis. Stochastics Monographs, vol. 5, pp. 389–414. Gordon & Breach Science Publishers, New York (1991)
Geman, H., El Karoui, N., Rochet, J.-C.: Changes of numeraire, changes of probability measure and option pricing. J. Appl. Probab. 32, 443–458 (1995)
Gerber H.U., Shiu, E.S.W.: Option pricing by Esscher transforms. Trans. Soc. Actuaries 46, 99–191 (1994)
Heath, D., Jarrow, A., Morton, A.: Bond pricing and the term structure of the interest rates; a new methodology. Econometrica 60(1), 77–105 (1992)
He, S.W., Wang, J.G., Yan, J.A.: Semimartingale theory and stochastic calculus. Science Press/CRC Press, Beijing/Boca Raton (1992)
Karatzas, I., Shreve, S.E.: Methods of Mathematical Finance. Springer, Berlin/Heidelberg/New York (1998)
Lamberton, D., Lapeyre, B.: Introduction to Stochastic Calculus Applied to Finance. Chapman & Hall, London (1996)
Lépingle, D., Mémin, J.: Sur l’intergrabilité uniforme des martingales exponentielles. Z.W. 42, 175–203 (1978)
Long, J.B.: The numeraire portfolio. J. Financ. Econ. 26, 29–69 (1990)
Protter, P.: Stochastic Integration and Differential Equations, 2nd edn. Springer, Berlin (2004)
Samuelson, P.: Risk and ambiguity: a fallacy of large numbers. Scientia 57, 108 (1963)
Schweizer, M.: On the minimal martingale measure and the Fóllmer- Schweizer decomposition. Stoch. Anal. Appl. 13, 573–579 (1994)
Yan, J.A., Zhang, Q., Zhang, S.: Growth optimal portfolio in a market driven by a jump-diffusion-like process or a Lévy process. Ann. Econ. Financ. 1, 101–116 (2000)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd. and Science Press
About this chapter
Cite this chapter
Yan, JA. (2018). Optimal Growth Portfolios and Option Pricing. In: Introduction to Stochastic Finance. Universitext. Springer, Singapore. https://doi.org/10.1007/978-981-13-1657-9_14
Download citation
DOI: https://doi.org/10.1007/978-981-13-1657-9_14
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-1656-2
Online ISBN: 978-981-13-1657-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)