A Limit Theorem for Financial Markets with Inert Investors

References

• Barber B., Odean T. The Internet and the investor. J. Econom. Perspectives (2001) 15(1):41–54Crossref, Google Scholar
• Barber B., Odean T. Online investors: Do the slow die first? Rev. Financial Stud. (2002) 15(2):455–487Crossref, Google Scholar
• Bayraktar E., Poor H. V. Arbitrage in fractal modulated Black-Scholes models when the volatility is stochastic. Internat. J. Theoret. Appl. Finance (2004) 8(3):1–18Google Scholar
• Bayraktar E., Poor H. V. Stochastic differential games in a non-Markovian setting. SIAM J. Control Optim. (2004) 43(5):1737–1756Crossref, Google Scholar
• Bayraktar E., Poor H. V., Sircar R. Estimating the fractal dimension of the S&P 500 index using wavelet analysis. Internat. J. Theoret. Appl. Finance (2004) 7(5):615–643Crossref, Google Scholar
• Bianchi S. Pathwise identification of the memory function of multifractional Brownian motion with applications to finance. Internat. J. Theoret. Appl. Finance (2005) 8:255–281Crossref, Google Scholar
• Billingsley P.Convergence of Probability Measures (1968) (John Wiley & Sons, New York) Google Scholar
• Bingham N. H., Goldie C. M., Teugels J. L.Regular Variation (1987) (Cambridge University Press, Cambridge, UK) Crossref, Google Scholar
• Brandt A., Franken P., Lisek B.Stationary Stochastic Models (1990) (John Wiley & Sons, New York) Google Scholar
• Brock W. A., Hommes C. A rational route to randomness. Econometrica (1997) 65(5):1059–1095Crossref, Google Scholar
• Brock W. A., Hommes C. Heterogeneous belief and routes to chaos in a simple asset pricing model. J. Econom. Dynam. Control (1998) 22:1235–1274Crossref, Google Scholar
• Cheridito P. Mixed fractional Brownian motion. Bernoulli (2001) 7(6):913–934Crossref, Google Scholar
• Cheridito P. Arbitrage in fractional Brownian motion models. Finance Stochastics (2003) 7(4):533–553Crossref, Google Scholar
• Choi J., Laibson D., Metrick A. How does the Internet affect trading? Evidence from investor behavior in 401(k) plans. J. Financial Econom. (2002) 64:397–421Crossref, Google Scholar
• Çinlar E. Markov renewal theory: A survey. Management Sci. (1975) 21:727–752Link, Google Scholar
• Çinlar E.Introduction to Stochastic Processes (1975) (Prentice-Hall, Englewood Cliffs, NJ) Google Scholar
• Cont R. Empirical properties of asset returns: Stylized facts and statistical issues. Quant. Finance (2001) 1:223–236Crossref, Google Scholar
• Cont R., Bouchaud J.-P. Herd behavior and aggregate fluctuations in financial markets. Macroeconomic Dynam. (2000) 4:170–196Crossref, Google Scholar
• Cutland N. J., Kopp P. E., Willinger W. Stock price returns and the Joseph effect: A fractional version of the Black-Scholes model. Progress in Probab. (1995) 36:327–351Google Scholar
• Ding Z., Granger C. W. J., Engle R. F. A long memory property of stock market returns and a new model. J. Empirical Finance (1993) 1:83–106Crossref, Google Scholar
• Dow J., Werlang S. Uncertainty aversion, risk aversion, and the optimal choice of portfolio. Econometrica (1992) 60(1):197–204Crossref, Google Scholar
• Duffie D., Protter P. From discrete- to continuous-time finance: Weak convergence of the financial gain process. Math. Finance (1992) 2(1):1–15Crossref, Google Scholar
• Duffield N. G., Whitt W. A source traffic model and its transient analysis for network control. Stochastic Models (1998) 14:51–78Crossref, Google Scholar
• Duffield N. G., Whitt W., Park K., Willinger W. Network design and control using on-off and multi-level source traffic models with heavy-tailed distributions. Self-Similar Network Traffic and Performance Evaluation (1998) (John Wiley & Sons, Boston, MA) 421–445Google Scholar
• Föllmer H. Stock price fluctuations as a diffusion model in a random environment. Philos. Trans. Roy. Soc. London A (1994) 374:471–483Crossref, Google Scholar
• Föllmer H., Schweizer M. A microeconomic approach to diffusion models for stock prices. Math. Finance (1993) 3:1–23Crossref, Google Scholar
• Föllmer H., Horst U., Kirman A. Equilibria in financial markets with heterogeneous agents: A new perspective. J. Math. Econom. (2004) 41(1–2):123–155Crossref, Google Scholar
• Gaigalas R., Kaj I. Convergence of scaled renewal processes and a packet arrival model. Bernoulli (2003) 9:671–703Crossref, Google Scholar
• Garman M. Market microstructure. J. Financial Econom. (1976) 3:257–275Crossref, Google Scholar
• Heath D., Resnick S., Samorodnitsky G. Heavy tails and long range dependence in on-off processes and associated fluid models. Math. Oper. Res. (1996) 23:145–165Link, Google Scholar
• Horst U. Financial price fluctuations in a stock market model with many interacting agents. Econom. Theory (2004) 25(4):917–932Google Scholar
• Jacod J., Shiryaev A.Limit Theorems for Stochastic Processes (1987) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
• Jelenkovic P. R., Lazar A. A. Subexponential asymptotics of a Markov-modulated random walk with queueing applications. J. Appl. Probab. (1998) 35:325–347Crossref, Google Scholar
• Kahneman D., Tversky A. Prospect theory: An analysis of decision under risk. Econometrica (1979) 47:263–291Crossref, Google Scholar
• Klüppelberg C., Kühn C. Fractional Brownian motion as a weak limit of Poisson shot noise processes—With applications to finance. Stochastic Processes Their Appl. (2004) 113:333–351Crossref, Google Scholar
• Kruk L. Functional limit theorems for a simple auction. Math. Oper. Res. (2003) 28(4):716–751Link, Google Scholar
• Kurtz T. G., Protter P. Weak limit theorems for stochastic integrals and stochastic differential equations. Ann. Probab. (1991) 19(3):1035–1070Crossref, Google Scholar
• Lin S. J. Stochastic analysis of fractional Brownian motions. Stochastics Stochastics Rep. (1995) 55:121–140Crossref, Google Scholar
• Levy J. B., Taqqu M. S. Renewal reward processes with heavy-tailed inter-renewal times and heavy-tailed rewards. Bernoulli (2000) 6:23–44Crossref, Google Scholar
• Lux T. The socio-economic dynamics of speculative markets: Interacting agents, chaos, and the fat tails of return distributions. J. Econom. Behav. Organ. (1998) 33:143–165Crossref, Google Scholar
• Lux T., Marchesi M. Volatility clustering in financial markets: A microsimulation of interacting agents. Internat. J. Theoret. Appl. Finance (2000) 3(4):675–702Crossref, Google Scholar
• Madrian B., Shea D. The power of suggestion: Inertia in 401(k) participation and savings behavior. Quart. J. Econom. (2001) CXVI(4):1149–1187Crossref, Google Scholar
• Mandelbrot B. B.Fractals and Scaling in Finance (1997) (Springer-Verlag, New York) Crossref, Google Scholar
• Mikosch T., Resnick S., Rootzén S. I., Stegeman A. Is network traffic approximated by stable Levy motion or fractional Brownian motion? Ann. Appl. Probab. (2002) 12:23–68Crossref, Google Scholar
• New York Stock Exchange Shareownership2000. (2000) . http://www.nyse.com/marketinfo/1022949657949.htmlGoogle Scholar
• O’Hara M.Market Microstructure Theory (1995) (Blackwell Publishing, Malden, MA) Google Scholar
• Protter P.Stochastic Integration and Differential Equations (1990) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
• Rogers L. C. G. Arbitrage with fractional Brownian motion. Math. Finance (1997) 7(1):95–105Crossref, Google Scholar
• Shefrin H., Statman M. The disposition to sell winners too early and ride losers too long: Theory and evidence. J. Finance (1985) XL(3):777–790Crossref, Google Scholar
• Simonsen M., Werlang S. Subadditive probability and portfilo inertia. Revista Econometrica (1991) 11:1–19Google Scholar
• Sottinen T. Fractional Brownian motion, random walks and binary market models. Finance Stochastics (2001) 5:343–355Crossref, Google Scholar
• Taqqu M. S., Levy J. B., Eberlein E., Taqqu M. S. Using renewal processes to generate long-range dependence and high variability. Dependence in Probability and Statistics (1986) (Birkhauser, Boston, MA) 73–89Crossref, Google Scholar
• Taqqu M. S., Willinger W., Sherman R. Proof of a fundamental result in self-similar traffic modeling. Comput. Comm. Rev. (1997) 27:5–23Crossref, Google Scholar
• Whitt W.Stochastic Process Limits: An Introduction to Stochastic-Process Limits and Their Application to Queues (2002) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar