an introduction to evolutionary computation

... (2000), Foster and Kesselman (2003), and Abbas (2004) 1.1 Computation and science Modern societies are not the only ones to rely on computation Ancient societies also had to deal with quantifying ... programming language Programming languages can be divided into two major categories: low-level languages designed to work with the given hardware, and high-level languages that are not related to any ... BigInteger and BigDecimal classes that allow us to perform computations with integers and floating-point numbers to any accuracy This is an important feature and has opened the door to better scientific...

Ngày tải lên: 05/03/2014, 11:21

... goes to Luna Han, Editor, and Danielle Lacourciere, Associate Managing Editor, of John Wiley & Sons This book is dedicated to Alice C Stan Tsai Ottawa, Ontario, Canada An Introduction to Computational ... to be executed A procedure language such as FORTRAN and C enables a programmer to communicate with many different machines in the same language, and it is easier to comprehend than machine language ... less significant and the method is more specific 2.1.2 Analysis of Variance, ANOVA We need to become familiar with the topic of analysis of variance, often abbreviated ANOVA, in order to test the...

Ngày tải lên: 08/04/2014, 12:40

... http://www.cis.ohio-state.edu/~gurari/theory-bk/theory-bk-onese3.html An execution sequence is said to be an accepting computation if it terminates due to an accept command An execution sequence is said to be a nonaccepting computation or a rejecting computation ... no accepting computations An execution sequence is said to be a computation if it is an accepting computation or a nonaccepting computation A computation is said to be a halting computation if ... their useful comments, and for allowing me the opportunities to teach the material I am also very grateful to an anonymous referee and to many students whose feedback guided me to the current exposition...

Ngày tải lên: 12/05/2014, 03:28

... = 50 and Nt = 500, so k = × 10−3 and h = 0.2, we found that err0 = 1.5 × 10−3 for FTCS and err0 = 1.7 × 10−3 for BTCS With Crank– Nicolson we were able to reduce Nt to 50, so k = × 10−2 , and ... which simplifies to ≤ ν sin2 ( βh) ≤ 2 For βh ∈ [−π, π] the quantity sin2 ( βh) takes values between and 1, and hence stability in the sense of von Neumann for FTCS is equivalent to ν ≤ (23.17) ... differencing in time The Crank–Nicolson method uses a clever trick to achieve second order in time without the need to deal with more than two time levels To derive the Crank–Nicolson method, we...

Ngày tải lên: 20/06/2014, 18:20

... Mark and Paul Glasserman (1998) Introduction to Chapter III: Volatility and correlation In Mark Broadie and Paul Glasserman, eds, Hedging with Trees London: Risk Books Brze´ niak, Zdislaw and Tomasz ... Hodder & Stoughton Lo, Andrew W and Craig MacKinlay (1999) A Non-Random Walk Down Wall Street Princeton, NJ: Princeton University Press Longstaff, F A and E S Schwartz (2001) Valuing American options ... Black–Scholes model: a note Journal of Finance, 38:227–230 Mantegna, Rosario N and H Eugene Stanley (2000) An Introduction to Econophysics: Correlations and Complexity in Finance Cambridge: Cambridge University...

Ngày tải lên: 20/06/2014, 18:20

... intentionally left blank AN INTRODUCTION TO FINANCIAL OPTION VALUATION Mathematics, Stochastics and Computation This is a lively textbook providing a solid introduction to financial option valuation ... accompanying stand-alone MATLAB code listing to illustrate a key idea The author has made heavy use of figures and examples, and has included computations based on real stock market data Solutions to ... contributions to a broad range of problems in numerical analysis AN INTRODUCTION TO FINANCIAL OPTION VALUATION Mathematics, Stochastics and Computation DESMOND J HIGHAM Department of Mathematics...

Ngày tải lên: 20/06/2014, 18:20

... samples and N(0,1) quantiles N(0,1) samples and U(0,1) quantiles 5 0 −5 −5 −5 −5 U(0,1) samples and N(0,1) quantiles U(0,1) samples and U(0,1) quantiles 1.5 0.5 −0.5 −5 −5 −1 −1 Fig 4.4 Quantile–quantile ... pseudo-random numbers Our justification for this omission is that random number generation is a highly advanced, active, research topic and it is unreasonable to expect non-experts to understand and ... reproducible, we set the random number generator seed to 100; that is, we used rand(‘state’,100) and randn(‘state’,100) 35 4.3 Statistical tests Table 4.2 Sample mean (4.1) and sample variance (4.2) using...

Ngày tải lên: 20/06/2014, 18:20

... known to investors, and hence any change in the price is due to new information We may build this into our model by adding a random ‘fluctuation’ increment to the interest rate equation and making ... data analysis Many exchanges have informative websites, including the American Stock Exchange: www.amex.com/, the Chicago Board Options Exchange: www cboe.com/Home/, the London Stock Exchange: ... way to compute a quantile–quantile plot, as seen in Figures 4.4, 4.6 and 5.3 It is listed in Figure 5.4 We use MATLAB’s N(0, 1) pseudo-random number generator, randn The line samples = randn(M,1),...

Ngày tải lên: 20/06/2014, 18:20

... see (Rogers and Zane, 1999), for example A completely different approach is to abandon any attempt to understand the processes that drive asset prices (in particular to pay no heed to the efficient ... the company and has many insights into the practical issues involved in collecting and analysing vast amounts of financial data EXERCISES 7.1 7.2 Confirm the results (7.4) and (7.5) By analogy ... able to transform this knowledge into money Finance is consistent in its ability to build good models and consistent in its inability to make easy money The purpose of the model is to understand...

Ngày tải lên: 20/06/2014, 18:20

... for a put option and In these new variables, d1 and d2 in (8.20) and (8.21) simplify to d1 = m τ + τ and d2 = m τ − , τ (11.1) and, from (8.19) and (8.24), the re-scaled call and put values become ... points to make (i) Formulas (12.2) and (12.4) were derived without any reference to the idea of hedging to eliminate risk (ii) Formulas (12.2) and (12.4) were derived without any reference to the ... switches to Newton’s method to get the benefit of rapid convergence Also, the residual |F(xn )| gives a measure of how close xn is to a solution, and this can be incorporated into the stopping...

Ngày tải lên: 20/06/2014, 18:20

... showed that valuing an option can be regarded as computing an expected value The idea of using pseudo-random number generators to compute estimates of expected values was touched on in Chapter ... two threads together and introduce the Monte Carlo approach to valuing an option As we will see in Chapter 19, this provides a powerful means to compute option values in cases where no analytical ... approximately an N(0, 1) random variable scaled √ by b/ M This suggests that sampling a M for large M should give an approxima√ tion to a that is correct to O(1/ M) We can make this argument more quantitative...

Ngày tải lên: 20/06/2014, 18:20

... reach, and puts a strain on computational methods 18.2 American call and put An American option is like a European option except that the holder may exercise at any time between the start date and ... • American call and put equivalence of European and American call Black–Scholes for American put binomial method for American options optimal exercise boundary Monte Carlo for American options ... superimposed To emphasize that large deltas can arise, we chose an asset that stumbles towards the strike price E near expiry The ‘near infinite’ deltas close to expiry are too much for the plotter to handle...

Ngày tải lên: 20/06/2014, 18:20

... for a range of strike prices and expiry times These prices relate to American, rather than European, options Americans are introduced in Chapter 18 For the moment we note that an American call ... simply purchasing the shares On the other hand, if you are the owner of an American company that is committed to purchasing a factory in Germany for an agreed price in euros in three 1.2 Why we ... including • what range of expiry dates and exercise prices are typically offered, • how dividends and stock splits are dealt with, and • how money and products actually change hands Section 5.5...

Ngày tải lên: 21/06/2014, 07:20

... see (Rogers and Zane, 1999), for example A completely different approach is to abandon any attempt to understand the processes that drive asset prices (in particular to pay no heed to the efficient ... the company and has many insights into the practical issues involved in collecting and analysing vast amounts of financial data EXERCISES 7.1 7.2 Confirm the results (7.4) and (7.5) By analogy ... able to transform this knowledge into money Finance is consistent in its ability to build good models and consistent in its inability to make easy money The purpose of the model is to understand...

Ngày tải lên: 21/06/2014, 07:20

... 191 Up–and–out European Call value E B S Fig 19.3 Time-zero up-and-out call value (19.5) as a function of S payoff cannot exceed B − E, and hence can be bought for much less than the European version ... is large, since there would be no payoff, it cannot be worthwhile to exercise an American put; it is optimal to hold on to the option On the other hand, in the limit S → 0, the payoff from exercising ... deals with points (i) and (iii) 180 American options 18.6 Monte Carlo for an American put We have seen that the binomial method has a natural extension from European to American options The same...

Ngày tải lên: 21/06/2014, 07:20

... and it follows immediately that if X and Y are independent then cov(X, Y ) = Loosely, from (21.1), if the covariance is positive then X and Y tend to be smaller than their means or larger than ... equivalent to sampling from an N((µ − σ ) t, σ t) distribution Hence, we could use a Monte Carlo approach to estimate the mean and variance Suppose that t = tn is the current time and that the ... M) means making more calls to a pseudorandom number generator In the above context, though, taking more samples means looking up more data There are two natural ways to this (1) Keep t fixed and...

Ngày tải lên: 21/06/2014, 07:20

... end aM = mean(V); bM = std(V); conf = [aM - 1.96*bM/sqrt(M), aM + 1.96*bM/sqrt(M)] aManti = mean(Vanti); bManti = std(Vanti); confanti = [aManti - 1.96*bManti/sqrt(M), aManti + 1.96*bManti/sqrt(M)] ... rather than about , the antithetic estimate uses −Ui , rather than − Ui Of course, −Ui is also an N(0, 1) random variable The above analysis that gave us (21.16) can then be repeated to give ... 21.6 Normal case 221 when f is monotonic In words: For monotonic f , the variance in the antithetic sample is always less than or equal to half that in the standard sample Of course, this is only...

Ngày tải lên: 21/06/2014, 07:20

... = 50 and Nt = 500, so k = × 10−3 and h = 0.2, we found that err0 = 1.5 × 10−3 for FTCS and err0 = 1.7 × 10−3 for BTCS With Crank– Nicolson we were able to reduce Nt to 50, so k = × 10−2 , and ... which simplifies to ≤ ν sin2 ( βh) ≤ 2 For βh ∈ [−π, π] the quantity sin2 ( βh) takes values between and 1, and hence stability in the sense of von Neumann for FTCS is equivalent to ν ≤ (23.17) ... differencing in time The Crank–Nicolson method uses a clever trick to achieve second order in time without the need to deal with more than two time levels To derive the Crank–Nicolson method, we...

Ngày tải lên: 21/06/2014, 07:20

... Mark and Paul Glasserman (1998) Introduction to Chapter III: Volatility and correlation In Mark Broadie and Paul Glasserman, eds, Hedging with Trees London: Risk Books Brze´ niak, Zdislaw and Tomasz ... Hodder & Stoughton Lo, Andrew W and Craig MacKinlay (1999) A Non-Random Walk Down Wall Street Princeton, NJ: Princeton University Press Longstaff, F A and E S Schwartz (2001) Valuing American options ... Black–Scholes model: a note Journal of Finance, 38:227–230 Mantegna, Rosario N and H Eugene Stanley (2000) An Introduction to Econophysics: Correlations and Complexity in Finance Cambridge: Cambridge University...

Ngày tải lên: 21/06/2014, 07:20

... (2000), Foster and Kesselman (2003), and Abbas (2004) 1.1 Computation and science Modern societies are not the only ones to rely on computation Ancient societies also had to deal with quantifying ... programming language Programming languages can be divided into two major categories: low-level languages designed to work with the given hardware, and high-level languages that are not related to any ... BigInteger and BigDecimal classes that allow us to perform computations with integers and floating-point numbers to any accuracy This is an important feature and has opened the door to better scientific...

Ngày tải lên: 29/06/2014, 10:20