A CONTINUOUS TIME APPROXIMATION OF AN EVOLUTIONARY STOCK MARKET MODEL

Boris Buchmann () and Stefan Weber ()
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Boris Buchmann: Centre of Excellence for Mathematics and Statistics of Complex Systems, Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia
Stefan Weber: School of Operations Research and Information Engineering, Cornell University, 279 Rhodes Hall, Ithaca, NY 14853, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2007, vol. 10, issue 07, 1229-1253

Abstract: We derive a continuous time approximation of the evolutionary market selection model of Blume and Easley (1992). Conditions on the payoff structure of the assets are identified that guarantee convergence. We show that the continuous time approximation equals the solution of an integral equation in a random environment. For constant asset returns, the integral equation reduces to an autonomous ordinary differential equation. We analyze its long-run asymptotic behavior using techniques related to Lyapunov functions, and compare our results to the benchmark of profit-maximizing investors.

Keywords: Portfolio theory; evolutionary finance; continuous time Euler approximation; stochastic processes in random environments; Lyapunov function (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219024907004627

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