Skip to main content
Log in

Optimal dealer pricing under transaction uncertainty

  • Published:
Journal of Intelligent Manufacturing Aims and scope Submit manuscript

Abstract

Dealers in securities markets are standing ready immediately to trade certain amounts of securities at stated bid and ask prices. This paper assumes that the amount of transactions follows an uncertain mean-reverting process associated with the bid and ask prices. In order to maximize the dealer’s total wealth, an optimal dealer pricing model under transaction uncertainty is established. And the optimal bid price and ask price over time are derived. Finally, the variations of the optimal bid and ask prices with different parameters are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Benston, G. J., & Hagerman, R. L. (1974). Determinants of bid-asked spreads in the over-the-counter market. Journal of Financial Economics, 1(4), 353–364.

    Article  Google Scholar 

  • Chen, X., & Liu, B. (2010). Existence and uniqueness theorem for uncertain differential equations. Fuzzy Optimization and Decision Making, 9(1), 69–81.

    Article  Google Scholar 

  • Chen, X., & Gao, J. (2013). Uncertain term structure model of interest rate. Soft Computing, 17(4), 597–604.

    Article  Google Scholar 

  • Cohen, K. J., Maier, S. F., Schwartz, R. A., & Whitcomb, D. K. (1978). The returns generation process, returns variance, and the effect of thinness in securities markets. The Journal of Finance, 33(1), 149–167.

    Article  Google Scholar 

  • Demsetz, H. (1958). The cost of transacting. The Quarterly Journal of Economics, 82(1), 33–53.

  • Epps, T. W. (1976). The demand for brokers’ services: The relation between security trading volume and transaction cost. The Bell Journal of Economics, 7(1), 163–194.

  • Garman, M. B. (1976). Market microstructure. Journal of Financial Economics, 3(3), 257–275.

    Article  Google Scholar 

  • Goldman, M. B., & Beja, A. (1979). Market prices vs. equilibrium prices: Returns’ variance, serial correlation, and the role of the specialist. The Journal of Finance, 34(3), 595–607.

    Article  Google Scholar 

  • Ho, T., & Stoll, H. R. (1981). Optimal dealer pricing under transactions and return uncertainty. Journal of Financial Economics, 9(1), 47–73.

    Article  Google Scholar 

  • Kolmogoroff, A. (1933). Grundbegriffe der wahrscheinlichkeitsrechnung. Berlin: Springer.

  • Liu, B. (2007). Uncertainty theory (2nd ed.). Berlin: Springer.

    Google Scholar 

  • Liu, B. (2008). Fuzzy process, hybrid process and uncertain process. Journal of Uncertain Systems, 2(1), 3–16.

    Google Scholar 

  • Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.

    Google Scholar 

  • Liu, B. (2010). Uncertainty theory: A branch of mathematics for modeling human uncertainty. Berlin: Springer.

    Book  Google Scholar 

  • Liu, B. (2010). Uncertain risk analysis and uncertain reliability analysis. Journal of Uncertain Systems, 4(3), 163–170.

    Google Scholar 

  • Liu, B. (2013). Toward uncertain finance theory. Journal of Uncertainty Analysis and Applications, 1, 1–15.

    Article  Google Scholar 

  • Oldfield, G. S, Jr, Rogalski, R. J., & Jarrow, R. A. (1977). An autoregressive jump process for common stock returns. Journal of Financial Economics, 5(3), 389–418.

  • Schwartz, R. A., & Whitcomb, D. K. (1977). The time-variance relationship: Evidence on autocorrelation in common stock returns. The Journal of Finance, 32(1), 41–55.

    Article  Google Scholar 

  • Smidt, S. (1979). Continuous versus intermittent trading on auction markets. Journal of Financial and Quantitative Analysis, 14(04), 837–866.

    Article  Google Scholar 

  • Stoll, H. R. (1978). The supply of dealer services in securities markets. The Journal of Finance, 33(4), 1133–1151.

    Article  Google Scholar 

  • Stoll, H. R. (1978). The pricing of security dealer services: An empirical study of NASDAQ stocks. The Journal of Finance, 33(4), 1153–1172.

    Article  Google Scholar 

  • Tinic, S. M., & West, R. R. (1972). Competition and the pricing of dealer service in the over-the-counter stock market. Journal of Financial and Quantitative Analysis, 7(03), 1707–1727.

    Article  Google Scholar 

  • Yang, X., & Gao, J. (2013). Uncertain differential games with application to capitalism. Journal of Uncertainty Analysis and Applications. doi:10.1186/2195-5468-1-17.

  • Yao, K. (2013). A type of uncertain differential equations with analytic solution. Journal of Uncertainty Analysis and Applications. doi:10.1186/2195-5468-1-2

  • Yao, K., & Chen, X. (2013). A numerical method for solving uncertain differential equations. Journal of Intelligent and Fuzzy Systems, 25(3), 825–832.

    Google Scholar 

  • Zhu, Y. (2010). Uncertain optimal control with application to a portfolio selection model. Cybernetics and Systems: An International Journal, 41(7), 535–547.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Cheng Guo.

Additional information

This work was supported by National Natural Science Foundation of China (Grant No. 61374082).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guo, C., Gao, J. Optimal dealer pricing under transaction uncertainty. J Intell Manuf 28, 657–665 (2017). https://doi.org/10.1007/s10845-014-1002-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10845-014-1002-8

Keywords

Navigation