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 Tr. Mat. Inst. Steklova, 2002, Volume 237, Pages 143–148 (Mi tm327)

On Upper and Lower Prices in Discrete-Time Models

L. Rüschendorf

Albert Ludwigs University of Freiburg

Abstract: A simple convex ordering argument in the class of equivalent martingale measures is used to determine the upper and lower prices of a convex claim in a general discrete-time model ($N$-period model) with bounded components. Under an approximation condition, the upper price is given by the price in a related Cox–Ross–Rubinstein model. As an application, we discuss a discrete-time stochastic volatility model.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2002, 237, 134–139

Bibliographic databases:
UDC: 519.2+519.8
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Citation: L. Rüschendorf, “On Upper and Lower Prices in Discrete-Time Models”, Stochastic financial mathematics, Collected papers, Tr. Mat. Inst. Steklova, 237, Nauka, MAIK «Nauka/Inteperiodika», M., 2002, 143–148; Proc. Steklov Inst. Math., 237 (2002), 134–139

Citation in format AMSBIB
\Bibitem{Rus02} \by L.~R\"uschendorf \paper On Upper and Lower Prices in Discrete-Time Models \inbook Stochastic financial mathematics \bookinfo Collected papers \serial Tr. Mat. Inst. Steklova \yr 2002 \vol 237 \pages 143--148 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm327} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1976511} \zmath{https://zbmath.org/?q=an:1021.91033} \transl \jour Proc. Steklov Inst. Math. \yr 2002 \vol 237 \pages 134--139 

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This publication is cited in the following articles:
1. A. A. Gushchin, É. Mordecki, “Bounds on Option Prices for Semimartingale Market Models”, Proc. Steklov Inst. Math., 237 (2002), 73–113
2. Bergenthum J., Ruschendorf L., “Comparison of option prices in semimartingale models”, Finance and Stochastics, 10:2 (2006), 222–249
3. N. Josephy, L. Kimball, V. R. Steblovskaya, A. V. Nagaev, M. Pasnievskii, “An algorithmic approach to non-self-financing hedging in a discrete-time incomplete market”, Discrete Math. Appl., 17:2 (2007), 189–207
4. Ivanov R.V., “On the pricing of American options in exponential Levy markets”, Journal of Applied Probability, 44:2 (2007), 409–419
5. Rokhlin D.B., “Martingale selection problem and asset pricing in finite discrete time”, Electronic Communications in Probability, 12 (2007), 1–8
6. A. Jurlewicz, A. Wyłomańska, P. Żebrowski, “Financial data analysis by means of coupled continuous-time random walk in Rachev-Ruschendorf model”, Acta Physica Polonica A, 114:3 (2008), 629–635
7. Courtois C., Denuit M., “Convex bounds on multiplicative processes, with applications to pricing in incomplete markets”, Insurance Mathematics & Economics, 42:1 (2008), 95–100
8. A. Jurlewicz, A. Wyłomańska, P. Żebrowski, “Coupled continuous-time random walk approach to the Rachev-Ruschendorf model for financial data”, Physica A-Statistical Mechanics and Its Applications, 388:4 (2009), 407–418
9. D. B. Rokhlin, “Recurrence relations for price bounds of contingent claims in discrete time market models”, Theory Probab. Appl., 56:1 (2012), 72–95
10. Nakajima R., Kumon M., Takemura A., Takeuchi K., “Approximations and asymptotics of upper hedging prices in multinomial models”, Japan Journal of Industrial and Applied Mathematics, 29:1 (2012), 1–21
11. Tkalinski T.J., “Convex Hedging of Non-Superreplicable Claims in Discrete-Time Market Models”, Math. Method Oper. Res., 79:2 (2014), 239–252
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