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Mathematics and Financial Economics

Erschienen in:

01.06.2015

A note on utility-based pricing in models with transaction costs

verfasst von: Mark H. A. Davis, Daisuke Yoshikawa

Erschienen in: Mathematics and Financial Economics | Ausgabe 3/2015

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Abstract

This paper considers the utility-based and indifference pricing in a market with transaction costs. The utility maximization problem, including contingent claims in the market with transaction costs, has been widely researched. In this paper, closely following the results of Bouchard (Financ Stoch 6:495–516, 2002), we consider the market equilibrium of contingent claims. This is done by specifying the utility function as exponential utility and, thus, determining equilibrium in the market with transaction costs. Unlike Davis and Yoshikawa (Math Finan Econ, 2015), we use the strong assumption to deduce the equilibrium at which trade does not occur (zero trade equilibrium). It implicitly shows that transaction costs may generate a non-zero trade equilibrium under a weaker assumption.

Vorheriger Artikel A note on utility-based pricing

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By introducing ${\mathcal {X}}_U(x)$, Bouchard proves the existence of a solution under looser conditions; that is, he addresses the problem $\sup _{X^{L} \in {\mathcal {X}}_U(x)} {\mathbb {E}}U[l(X^{x,L} - B q)]$. The definition of ${\mathcal {X}}_U(x)$ is given as follows: for $X \in L^0\big ({\mathcal {F}}_T,{\mathbb {R}}^d\big )$, which is a member of ${\mathcal {X}}_U(x)$, there exists a sequence $\big (X_k\big )_k \in {\mathcal {X}}(x)$ such that

$$\begin{aligned} X_k \rightarrow X \ P-a.s. \text{ and } {\mathbb {E}}\bigg [U\big (l(X_k - B)\big )\bigg ] \rightarrow {\mathbb {E}}\bigg [U\big (l(X - B)\big )\bigg ],\ \text{ as } k \rightarrow \infty . \end{aligned}$$

Benedetti, G., Campi, L.: Multivariate utility maximization with proportional transaction costs and random endowment. SIAM J. Control Optim. 50, 1283–1308 (2011)CrossRefMathSciNet

Bouchard, B.: Stochastic control and applications in mathematical finance. Ph.D. Dissertation, Université Paris IX (2000)

Bouchard, B.: Utility maximization on the real line under proportional transaction costs. Financ. Stoch. 6, 495–516 (2002)CrossRefMATHMathSciNet

Bouchard, B., Kabanov, Y., Touzi, N.: Option pricing by large risk aversion utility under transaction costs. Decis. Econ. Financ. 24, 127–136 (2001)CrossRefMATHMathSciNet

Campi, L., Owen, M.: Multivariate utility maximization with proportional transaction costs. Financ. Stoch. 15, 461–499 (2011)CrossRefMATHMathSciNet

Cvitaníc, J., Wang, H.: On optimal terminal wealth under transaction costs. J. Math. Econ. 35, 223–231 (2001)CrossRefMATH

Davis, M.A.H., Yoshikawa, D.: A note on utility-based pricing. Math. Finan. Econ. (forthcoming)

Henderson, V.: Valuation of claims on non-traded assets using utility maximization. Math. Financ. 12, 351–373 (2002)CrossRefMATH

Hugonnier, J., Kramkov, D.: Optimal investment with random endowments in incomplete markets. Ann. Appl. Probab. 14(2), 845–864 (2004)CrossRefMATHMathSciNet

10.

Ihara, S.: Information Theory for Continuous System. World Scientific, Singapore (1993)CrossRef

11.

Kabanov, Y.: Hedging and liquidation under transaction costs in currency markets. Financ. Stoch. 3, 237–248 (1999)CrossRefMATHMathSciNet

12.

Kabanov, Y., Last, G.: Hedging under transaction costs in currency markets: a continuous-time model. Math. Financ. 12, 63–70 (2002)CrossRefMATHMathSciNet

13.

Kabanov, Y., Safarian, M.: Market with Transaction Costs. Springer, Berlin (2010)CrossRef

14.

Kamizono, K.: Multivariate utility maximization under transaction costs. In: Akahori, J., Ogawa, S., Watanabe, S. (eds.) Stochastic Processes and Applications to Mathematical Finance: Proceedings of the Ritsumeikan International Symposium, pp. 133–149. World Scientific, Singapore (2004)

15.

Rockafellar, R.: Convex Analysis. Princeton, New Jersy (1970)MATH

16.

Schachermayer, W.: The fundamental theorem of asset pricing under proportional transaction costs in finite discrete time. Math. Financ. 14, 19–48 (2004)CrossRefMATHMathSciNet

Titel: A note on utility-based pricing in models with transaction costs
verfasst von: Mark H. A. Davis
Daisuke Yoshikawa
Publikationsdatum: 01.06.2015
Verlag: Springer Berlin Heidelberg
Erschienen in: Mathematics and Financial Economics / Ausgabe 3/2015
Print ISSN: 1862-9679
Elektronische ISSN: 1862-9660
DOI: https://doi.org/10.1007/s11579-015-0143-7