Abstract
The existence of a linear equilibrium in Kyle’s model of market making with multiple, symmetrically informed strategic traders is implied for any number of strategic traders if the joint distribution of the underlying exogenous random variables is elliptical. The reverse implication has been shown for the case in which the random variables are independent and have finite second moments. Here we extend this result to the case in which the underlying random variables are not necessarily independent and their joint distribution is determined by its moments.
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References
Bagnoli M., Viswanathan S., Holden C. (2001). On the existence of linear equilibria in models of market making. Math Finance 11, 1–31
Berg, C.: Recent results about moment problems. In: Probability measures on groups and related structures. In: Heyer H. (ed.) XI Proceedings Oberwolfach 1994, World Scientific, Singapore (1995)
Berg C., Thill M. (1991). Rotation invariant moment problems. Acta Math 167, 207–227
Bélisle C., Massé J.-C., Ransford T. (1997). When is a probability measure determined by infinitely many projections?. Ann Prob 25, 767–786
Billingsley P. (1995). Probability and measure, 3rd edn. Wiley, New York
Chamberlain G. (1983). A characterization of the distributions that imply mean-variance utility functions. J Econ Theory 29, 185–201
Cramér H., Wold H. (1936). Some theorems on distribution functions. J London Math Soc 11, 290–294
Fang K.-T., Kotz S., Ng K.-W. (1990). Symmetric multivariate and related distributions. Chapman and Hill, New York
Foster F., Viswanathan S. (1993). The effect of public information and competition on trading volume and price volatility. Rev Finan Stud 6, 23–56
Gilbert W.M. (1955). Projections of probability distributions. Acta Math Acad Sci Hungar 6, 195–198
Hardin C. (1982). On the linearity of regression. Z Wahrscheinlichkeitstheorie und verwandte Gebiete 61, 291–302
Kyle A. (1985). Continuous auctions and insider trading. Econometrica 53, 1315–1335
Lukacs E., Laha R. (1969). Applications of characteristic functions. Griffin, London
Nöldeke G., Tröger T. (2001). Existence of linear equilibria in the Kyle model with multiple informed traders. Econ Lett 72, 159–164
Nöldeke G., Tröger T. On the existence of linear equilibria in the Rochet–Vila model of market making. Bonn Econ Discussion Paper 19/2004 (2004)
O’Hara M. (1995). Market microstructure theory. Basil Blackwell, Cambridge, MA
Peterson L.C. (1982). On the relation between the multidimensional moment problem and the one-dimensional moment problem. Mathematica Scandinavica 51, 361–366
Rochet J.-C., Vila J.-L. (1994). Insider trading without normality. Rev Econ Stud 61, 131–152
Shohat J.A., Tamarkin J.D. (1950). The problem of moments. Amer Math Soc Colloquium Publ, New York
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We thank two anonymous referees for their comments. Financial support by the Deutsche Forschungsgemeinschaft, SFB-TR 15, is gratefully acknowledged.
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Nöldeke, G., Tröger, T. A characterization of the distributions that imply existence of linear equilibria in the Kyle-model. Annals of Finance 2, 73–85 (2006). https://doi.org/10.1007/s10436-005-0024-9
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DOI: https://doi.org/10.1007/s10436-005-0024-9