130 Oct Radial Basis Function RBF Efficient Market Hypothesis Fama ) 4) 1 Fig. 1 Utility function. 2 Fig. 2 Value function. (1) (2)

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1 Vol. 47 No. SIG 14(TOM 15) Oct RBF 2 Effect of Stock Investor Agent According to Framing Effect to Stock Exchange in Artificial Stock Market Zhai Fei, Shen Kan, Yusuke Namikawa and Eisuke Kita Several psychological biases should be taken into consideration in the actual stock exchange. In this paper, we discuss the effect of the framing effect to it. The stock investor agent is defined by using the RBF neural network. The prediction of the agent shows that the agent behaviour follows the framing effect. The stock exchange by the agents is performed in the artificial market. The characteristics of the stock price fluctuations in the actual and artificial markets are compared in order to discuss the effect to the agents accodring to the framing effect. Artificial markets are comstructed with the agents of which prediction rules are learned by short and long moving average data. In the market of many agents learned with long-run moving average data, the features of the stock price fluctuation are similar to them of the actual market. 1. 1) 20 1 Graduate School of Information Sciences, Nagoya University NTT NTT Data Co. 2) 129

2 130 Oct Radial Basis Function RBF Efficient Market Hypothesis Fama ) 4) 1 Fig. 1 Utility function. 2 Fig. 2 Value function. (1) (2) (3) (4) (5) Behavioral Finance

3 Vol. 47 No. SIG 14(TOM 15) 131 5),6) 1 2 7) reference point 8) 8) 10) 2.3 7) (1) anchoring adjustment (2) hindsight bias (3) representativeness heuristics (4) availability bias (5) framing effect ) 2),10) (1) 3 Fig. 3 Artificial market model.

4 132 Oct (2) 4 RBF Fig. 4 RBF neural network. (3) 3.2 RBF RBF RBF RBF 4 1 F (x) Φ i (x) (1) 12),13) n F (x) = ω i Φ i (x) (1) i=1 Φ i (x) (2) ( Φ i (x) =exp (x c ) i) 2 (2) σi 2 Φ i (x) c i σ i i ω i 14) RBF 3 c i σ i ω i RBF c i σ i 2 RBF c i k-means k ω i k-means k-means N x i i =1 n k G i i =1 k 12),13) k-means Step1 k c i Step2 c i (3) (4) x i G i ( T ) 1 2 D(x, c) = (x k c k ) 2 (3) k=1 D(x i,c j ) <D(x i,c l ) j l (4) Step3 (5) c i c i = 1 x j (5) G i x j G i G i G i Step4 c j Step k k

5 Vol. 47 No. SIG 14(TOM 15) 133 Moving Average MA J.E. 15) t P t n 5 Fig. 5 Back propagation. σ i 12),13) i σ i c i k σ i = 1 k c i c j (6) k j=1 c j j =1...k c i k k ω i E E (7) y i o i (w i ) E ω i (ω i ) old (ω i ) old ω i (ω i ) old ω i (8) (ω i ) new 13) E = 1 n (y i o i (w i )) 2 (7) 2 i (ω i ) new =(ω i ) old + ω i (8) (ω i ) old E ω i η ω i (9) ω i = η E ω i (9) η η 3.3 RBF MA P t y i MA = P 0 + P P n 1 (10) n ,000,000 10,000 P t (1) P t >P t 1 O t / O t =(M t Pt ) P t P t 1 α (11) P t 1 (2) P t <P t 1 O t O t = S t P t 1 P t P t 1 α (12) P t P t t t M t t S t t α 3.5 S t = S t + Ot (13) M t = M t P t Ot (14)

6 134 Oct S t = S t Ot (15) M t = M t + P t Ot (16) P t O t M t S t M t t t t t S t t O t Ot Ot RBF ) ),17) 3.7 RBF t t max t rel t rel t rel =30 (1) (2) RBF (3) t t 0 (4) RBF (5) (6) (7) (8) (9) t t +1 (10) Mod(t, t rel )=0(4) Mod(t, t rel ) t t rel (11) t<t max (5) RBF

7 Vol. 47 No. SIG 14(TOM 15) Fig. 6 Stock price with increasing trend η =0.6 RBF Real price Agent1 Agent Fig. 7 Prediction of Agent 1 for stock price with increasing trend. 2 Fig. 8 Prediction of Agent 2 for stock price with increasing trend. Fig. 9 9 Stock price with decreasing trend

8 136 Oct Fig. 10 Prediction of Agent 1 for stock price with decreasing trend Fig. 11 Prediction of Agent 2 for stock price with decreasing trend ,000 1,000, n n =1, 2, % 2 25% % % 2 75%

9 Vol. 47 No. SIG 14(TOM 15) Fig. 12 Accuracy of predicted stock price in Market Fig. 16 Accuracy of predicted stock price in Market 5. Table 1 1 Average value of accuray of predicted stock price. Market Agent 1 Agent Fig. 13 Accuracy of predicted stock price in Market Fig. 17 Volume of dealing in Market Fig. 14 Accuracy of predicted stock price in Market Fig. 15 Accuracy of predicted stock price in Market Fig. 18 Volume of dealing in Market

10 138 Oct Fig. 19 Volume of dealing in Market Fig. 22 Stock price and its volatility in Market Fig. 20 Volume of dealing in Market Fig. 23 Stock price and its volatility in Market Fig. 21 Volume of dealing in Market = 100 (%) (17) Fig. 24 Stock price and its volatility in Market

11 Vol. 47 No. SIG 14(TOM 15) Fig. 25 Stock price and its volatility in Market Fig. 27 Frequency distribution of volatility in Market Fig. 28 Frequency distribution of volatility in Market Fig. 26 Stock price and its volatility in Market ),18),19) IBM Fig. 29 Frequency distribution of volatility in Market Fig. 30 Frequency distribution of volatility in Market : 75 0 : Self-corelative coefficient of Stock Price: SSP

12 140 Oct σ PRo3S Fig. 31 Frequency distribution of volatility in Market IBM Fig. 32 Frequency distribution of IBM Stock price volatility (2003 Oct Feb.). 2 Table 2 Parameter of return. Parameter Real Market SSP SSC PRi1S PRo3S Table 3 Parameter estimated at artificial markets. Market Parameter SSP SSC PRi1S PRo3S Self-correlation coefficient of Stoch Change rate: SSC 1σ Probability of Return in 1 Sigma: PRi1S 3σ Probability of Return out of 3 Sigma: PRo3S 2 20) 5 3 SSP SSC 1σ PRi1S Radial Basis Function RBF COE

Vol. 47 No. SIG 14(TOM 15) 141 1) (2001). 2) (2003). 3) Fama, E.

4) Ingersoll, J.E.: Theory of Financial Decision Making, Rowman and Littlefield (1987). 5) Goldberg,J.andvonNitzsch,R.

7) (2001). 8) (2003). 9) Kahneman, D. and Tversky, A.: Prospect theory: An analysis of decisions under risk, Econometrica, Vol.

: Face recognition with radial basis function (rbf) neural networks, IEEE Trans.Neural Networks, Vol.13, No.3, pp.697 710 (2002).

13 Vol. 47 No. SIG 14(TOM 15) 141 1) (2001). 2) (2003). 3) Fama, E.: Efficient capital markets: A review of theory and empirical work, Journal of Finance, Vol.25, pp (1970). 4) Ingersoll, J.E.: Theory of Financial Decision Making, Rowman and Littlefield (1987). 5) Goldberg,J.andvonNitzsch,R.:Behavioral Finance, Finanz Buch Verlag GmbH (1999). 6) Shleifeer, A.: Inefficient Markets, OxfordUniversity Press (2000). 7) (2001). 8) (2003). 9) Kahneman, D. and Tversky, A.: Prospect theory: An analysis of decisions under risk, Econometrica, Vol.47, pp (1979). 10) (2003). 11) A. (2001). 12) (1997). 13) GA (2002). 14) Joo, M., Wu, S., Lu, J. and Lye, H.: Face recognition with radial basis function (rbf) neural networks, IEEE Trans.Neural Networks, Vol.13, No.3, pp (2002). 15) (2000). 16) (2003). 17) Vol.119, No.1, pp (2000). 18) (2004). 19) (1983). 20) ADG Vol.43, No.7, pp (2002). ( ) ( ) ( ) NTT BEM Trefftz Cellular Automata Trefftz IEEE ISBE

23_02.dvi

23_02.dvi Vol. 2 No. 2 10 21 (Mar. 2009) 1 1 1 Effect of Overconfidencial Investor to Stock Market Behaviour Ryota Inaishi, 1 Fei Zhai 1 and Eisuke Kita 1 Recently, the behavioral finance theory has been interested