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<ul> <li> </li> <li> </li> <li> <ul><li> ( ) </li></ul></li> <li> <ul><li>Blaise Pascal (1623-1662) </li></ul>Pierre de Fermat (1601-1665) 1654 Pascal Fermat </li> <li> Pascal Fermat <ul><li> 5 6 A 4 6 B 3 6 </li></ul><ul><li> A 3/4, B 1/4. </li></ul></li> <li> ( ) <ul><li>Jacob Bernoulli (1654-1705) </li></ul>1713 (Ars Conjectandi) </li> <li> <ul><li> 1 2 4 n n+1 </li></ul></li> <li> <ul><li>1738 </li></ul>Daniel Bernoulli 1700-1782) </li> <li> <ul><li>1944 </li></ul>John von Neumann (1903-1957) Oskar Morgenstern (1902-1977) </li> <li> <ul><li> ( x,y,p ) p x , (1- p ) y u (( x,y,p ))= pu ( x )+(1- p ) u ( y ). </li></ul></li> <li> <ul><li> ( x,y,p ) px +(1- p ) y </li></ul><ul><li>u (( x,y,p ))= pu ( x )+(1- p ) u ( y ) u ( px +(1- p ) y ) </li></ul><ul><li> ( ) &lt; &gt; </li></ul></li> <li> Arrow-Pratt <ul><li> u </li></ul><ul><li>- u / u Arrow (1965) Pratt (1964) </li></ul></li> <li> <ul><li> Allais (1953) </li></ul>Maurice Allais (1911-) 1986 </li> <li> Knight (1921) <ul><li>Knight = </li></ul><ul><li>Knight </li></ul>Frank Hyneman Knight (1885-1972) </li> <li> Arrow-Debreu <ul><li>1954 Arrow Debreu </li></ul><ul><li> Knight </li></ul>Kenneth J. Arrow 1921-) 1972 Gerard Debreu (1921-) 1983 </li> <li> Arrow (1953) <ul><li>Arrow </li></ul></li> <li> <ul><li> Harry Markowitz 1952 1973 Fisher Black Myron Scholes ( Robert Merton) Black-Scholes </li></ul></li> <li> 1990 Harry Markowitz, (1927-) Merton Miller, (1923-2000) Modigliani-Miller (MMT) William Sharpe, (1934-) CAPM) </li> <li> 1997 Fisher Black (1938-1995) 1973 Black-Scholes-Merton Robert Merton, (1944-) Myron Scholes, (1941-) </li> <li> Markowitz <ul><li>Markowitz </li></ul></li> <li> Markowitz </li> <li> Markowitz </li> <li> Markowitz </li> <li> Tobin <ul><li> Markowitz </li></ul><ul><li> Tobin (1958) </li></ul>James Tobin, (1918-) 1981 </li> <li> (CAPM) <ul><li>Sharpe (1964) Markowitz (Capital Asset Pricing Model, CAPM) </li></ul></li> <li> (CAPM) E : ( ) Cov: Var: </li> <li> <ul><li>Miller Modigliani (1958) M-M ( ) </li></ul>Franco Modigliani, (1918-) 1985 </li> <li> B-S <ul><li> Black-Scholes </li></ul></li> <li> Black Scholes Markowitz </li> <li> Black-Scholes </li> <li> Black-Scholes </li> <li> Black-Scholes <ul><li>c ( x,t ) x, t </li></ul><ul><li>K T r </li></ul><ul><li>N </li></ul></li> <li> Black-Scholes Black-Scholes </li> <li> Black-Scholes t = T t &lt; T K </li> <li> Black-Scholes </li> <li> ( ) </li> <li> Black-Scholes-Merton <ul><li> ( ) </li></ul><ul><li> ( ) </li></ul></li> <li> Black-Scholes-Merton <ul><li>The Black-Scholes option pricing model established the everyday use of mathematical models as essential tools in the world of finance, both in the classroom and on the trading floor. </li></ul><ul><li> Black-Sholes </li></ul></li> <li> ( ) <ul><li>The model offers a methodology to predict the seemingly unpredictable by using the lessons of complex mathematics and probability theory to forecast stock valuations, making it possible to successfully manage risk in the financial market. </li></ul></li> <li> ( ) <ul><li>In less than thirty years it has changed the course of economic theory and financial practice. </li></ul></li> <li> ( ) <ul><li>The work of Robert Merton, Fischer Black and Myron Scholes is the culmination of a series of discoveries and theories spanning the twentieth century. </li></ul><ul><li>Merton Black Scholes </li></ul></li> <li> ( ) <ul><li>From Louis Bachelier, an obscure French mathematician who wrote at the turn of the century, through the contributions of scholars such as Harry Markowitz, John Lintner, William Sharpe, Eugene Fama, Franco Modigliani, and Merton Miller, the quest to apply the lessons of probability theory to the stock market has been a key focus of twentieth-century American finance. </li></ul></li> <li> ( ) <ul><li> Bachelier Markowitz Lintner Sharpe Fama Modigliani Miller </li></ul><ul><li> Baker </li></ul></li> <li> <ul><li>Black-Scholes Stephen Ross (1940-) (1978) </li></ul> S J </li> <li> ( ) <ul><li> S S S </li></ul><ul><li> 1 S </li></ul></li> <li> ( ) </li> <li> ( ) <ul><li>1979 Cox, Ross Rubinstein Black-Scholes </li></ul></li> <li> <ul><li> Black-Scholes </li></ul><ul><li> (Fama, 1970) </li></ul>Eugene F. Fama (1939-) </li> <li> ( ) <ul><li> ( ) ( ) ( ) </li></ul></li> <li> </li> <li> Grossman-Stiglitz <ul><li> (Grossman-Stiglitz, 1980) </li></ul>Stanford J. Grossman Joseph E. Stiglitz </li> <li> <ul><li> 1997 10 50 50 </li></ul></li> <li> ( ) <ul><li> 49 50 </li></ul><ul><li> A A A A A </li></ul></li> <li> ( ) <ul><li> A B A B A B B A A B B A B A A B A B </li></ul><ul><li> A B C A B C : 50 50 </li></ul></li> <li> ( ) <ul><li> (1997) 50 </li></ul><ul><li> 1997 4 </li></ul></li> <li> ( ) <ul><li>-- Paulos, J. A., 1998, Once upon a Number, Basic Books. L.A.. ( J. A.,2001 ) </li></ul></li> <li> <ul><li> Markowitz </li></ul><ul><li> Black-Scholes-Merton </li></ul></li> <li> ( ) <ul><li>Black-Scholes-Merton </li></ul><ul><li>Black-Scholes-Merton </li></ul></li> </ul>