Overview:

This text is intended for students who have some knowledge about financial markets and have a background in mathematics through calculus and calculus-based probability. Some knowledge of linear programming and elementary optimization theory would also be useful.The aim is to present as much financial theory about securities markets as possible without requiring the advanced mathematics that is associated with continuous time models. The book is especially appropriate for undergraduate and first-year graduate students in the mathematical sciences as well as for advanced MBA and Ph.D. students in business. Masters level students studying financial engineering may find it appropriate to take a course based on this book while simulataneously, in other courses, studying stochastic calculus and other advanced mathematical topics. Practitioners may find the book useful for learning the financial theory in a rigorous yet accessible manner.

The English version of the book has had several printings. The first printing was in 1997. The second printing says "Reprinted 1997" on the back of the title page, and it and all subsequent printings indicate the subsection numbers and titles at the tops of all the odd pages (the first printing had different headings). The latest printing appeared in 2001. There are also Chinese and Japanese translations (see Book Ordering Information below).

Immediately below is ordering information and then the Table of Contents. Following that are three lists of typographical errors. The first list shows errors which exist in the first printing and which are corrected in all subsequent versions. The second list shows errors which exist in the second printing (and thus the first printing as well); all these errors are corrected in subsequent printings. Finally, the third list shows errors which exist in all printings (as of July 2003). Notification about additional errors as well as general comments will be gratefully received by the author at srpliska@uic.edu.

Solutions Manual Now Available For Instructors:

The book has exercises at the ends of the chapters, and a manual with full and complete solutions has recently been prepared. Instructors who adopt the book as a required text can obtain a free copy of the solutions manual by contacting directly the author.

Book Ordering Information:

• English Edition
• Blackwell Publishers, 350 Main Street, Malden MA 02148 (toll-free: 800-216-2522; fax: 617-388-8210)
• ISBN: 1-55786-945-6
• Or see the Amazon.com web page by clicking here
• Chinese Edition
• Economic Science Press (www.esp.com.cn)
• Translation Series of Methods and Modeling in Mathematical Finance
• ISBN: 7-5058-2995-5
• phone: 010-8819-1515  fax: 010-8819-1516 <fx@esp.com.cn>
• Japanese Edition
• www.kyoritsu-pub.co.jp
• ISBN:  4-320-09626-6

Chapter 1 Single Period Securities Markets

• Model Specifications
• Arbitrage and Other Economic Considerations
• Risk Neutral Probability Measures
• Valuation of Contingent Claims
• Complete and Incomplete Markets
• Risk and Return

• Optimal Portfolios and Viability
• Risk Neutral Computational Approach
• Consumption Investment Problems
• Mean-Variance Portfolio Analysis
• Portfolio Management with Short Sales Constraints and Similar Restrictions
• Optimal Portfolios in Incomplete Markets
• Equilibrium Models

• Model Specifications, Filtrations, and Stochastic Processes
• Return and Dividend Processes
• Conditional Expectation and Martingales
• Economic Considerations
• The Binomial Model
• Markov Models

• Contingent Claims
• European Options Under the Binomial Model
• American Options
• Complete and Incomplete Markets
• Forward Prices and Cash Stream Valuation
• Futures

• Optimal Portfolios and Dynamic Programming
• Optimal Portfolios and Martingale Methods
• Consumption-Investment and Dynamic Programming
• Consumption-Investment and Martingale Methods
• Maximum Utility from Consumption and Terminal Wealth
• Optimal Portfolios with Constraints
• Optimal Consumption-Investment with Constraints
• Portfolio Optimization in Incomplete Markets

• The Basic Term Structure Model
• Lattice, Markov Chain Models
• Yield Curve Models
• Forward Risk Adjusted Probability Measures
• Coupon Bonds and Bond Options
• Swaps and Swaptions
• Caps and Floors

• Finite Horizon Models
• Infinite Horizon Models

• page 3, line 13 from bottom: should be V_1 = (10/9)H_0 + (20/3)H_1
• page 4, line 4 of example 1.4: S_2(1) = 120/9, not 20/9
• page 12, line 1: change \Delta to \Omega
• page 110, first line of first display: superscript of "u" should be "X_{t+1} + N_t"
• page 110, third line of first display: insert a right square bracket at the end of the line
• page 123, last line of example 4.7: summation should be over all j<i
• page 132, line 8: add a vertical bar to the conditional expectation
• page 201, line preceding bottom display: should be r_1 = 0.06
• page 201, 5th line after (6.3): determined
• page 208, line 10 of section 6.2: delete the first "conditional"
• page 211, equation (6.10): change {Z^\tau}_{t-1} to {Z^\tau}_{t+1}
• page 212, first line following equation (6.15): change subscript of "r" from "t" to "\tau"
• page 213, line preceding (6.17): change (6.14) to (6.15)
• page 213, equation (6.17): change superscript of product from "t-1" to "t-2"
• page 214, second line of example 6.5: change subscript of r from "r+1" to "t+1"
• page 214, equation (6.18): add subscript "1" to summation index "i"
• page 240, 2 lines above (7.6): add superscript * to S_{t-1}
• page 241, 5 lines from top: insert "(\omega)>0" after probability in specification of the event
• page 241, 5 lines before (7.8): change "I will show how to actually constuct..." to "I will indicate how to construct..."
• page 250, 3 lines following display: b is an element of R^m, not R^n

• page 4, line 4 of example 1.4: S_2(1) = 120/9, not 20/9
• page 4, table in Example 1.4: the number in row n = 2 and column \omega_4 should be 12 (this is correct in first printing, but not in second)
• page 8, line 1: change subscript of last V-tilde from o (i.e., oh) to 0 (i.e., zero)
• page 13, line 29: change the symbol \phi for the empty set so it is the same as the symbol used in lines 19 and 35
• page 14, 7th line from bottom: change subscript of \omega from cap K to lower-case k
• page 26, line 3: change "column" to "row"
• page 29, first line of top display: delete superscript * on S_n(1) in numerator on RHS
• page 32, last line of note 7: change \rho_R_n to \sigma_R_n
• page 36, example 2.1, first line of table: in second column it should be S_n^*(0), not just S_n^*
• page 40, line 6: change 0.41490 to 0.41588
• page 41, line 21: change equation label from (2.4) to (2.14)
• page 42, equation (2.16): in third line of display, the subscript of B should be 1, not 0
• page 43, line 5: in third line of (2.18), the first term 10/C_0 should have a minus sign
• page 45, line 14: in first line of example 2.3, change u(C) to u(c), i.e., lower case c
• page 53, line 4: in the second display there is a 0.02 in the denominator which should be changed to 0.2
• page 53, line 14: the notation for the two partial derivatives should be improved
• page 53, last line of example 2.5: change 0.002 to 0.00021
• page 54, bottom line: in the denominator of the display, change the q to a 1
• page 55, equation (2.44): delete the delta(kappa) term in the numerator
• page 55, in the display between (2.44) and (2.45): delete the superfluous left paranthesis
• page 55, line 2 of Example 2.5: change (3.44) to (2.44)
• page 56, equation (2.46): change to ...= vB_1 ^kappa /L_kappa = vP/Q_kappa
• page 56, 4 lines before equation (2.48): change J(kappa) to J(v)
• page 56, equation (2.48): change J(kappa) to J(v)
• page 56, bottom line: change J(kappa) to J(v)
• page 61, line 4: the numerator of first term should be 4, not 1
• page 61, displayed formula for W(\omega): for \omega_3, change value from 2.076611 to 2.07611
• page 64, line 13 from bottom: change t = 1 to t = 0
• page 66, line 5: in the displayed equation, change subscript of S from N to n
• page 67, line 4: the sum on the RHS goes from i = 1 to I, not to n
• page 70, 8th line before exercise: change S_2 = 2000 to s_2 = 2000, i.e., make S lower case
• page 77, 2nd line of subsection: delete the slash (/)
• page 77, 11th line of subsection: change W(\omega) to X(\omega)
• page 80, last line: change H_n(1,\omega_i) to H_n(3,\omega_i) for i = 1, 2, 7, and 8
• page 81, line 14: the subscript of H should be n, not N
• page 83, 9th line from bottom: the subscript of V-star should be t, not n
• page 83, 8th line from bottom: on left side of this display, the subscript of V-star should be t, not n
• page 84, 1st line of section 3.2: change N = 1,... to n = 1,...
• page 84, equation (3.8): below the product sign it should be u = 1, not u - 1
• page 85, last line: the subscript of the last M should be upper-case N, not lower-case n
• page 86, 5th line from bottom: change R_0 to {R_n}
• page 88, line 7: change \Delta D(t) to \Delta D_n(t)
• page 88, line 17: on left side of equation, add superscript star (i.e.*) to R
• page 89, line 9: near end of display, insert P so it reads ...P{\omega}/P{A}
• page 90, expression (3.14): change all X to all A
• page 91, line 7: in the second line of display the subscript of script-F should be t, not 1
• page 93, line 10: in condition 1, insert a 0 so it reads ... > 0 for...
• page 97, line 3: insert right square bracket just before last vertical bar
• page 97, line 23: change (1+8r)/3 to (1+4r)/3 and change (2-8r)/3 to (2-4r)/3
• page 97, equation (3.24): the expectation should be conditioned on the time-t algebra script-F_t
• page 98, display (3.28): move the vertical bar to immediately before the script F_t
• page 105, line 16: change N_t to N_T. Also, in binomial coefficient it should be T+i, not T+1
• page 105, 7th line from bottom: change superscript of p from cap N to lower-case n
• page 111, line 4: change cap P to lower-case p so it's ...= p_i for 2T-1 parameters...
• page 113, 4th line after table: change ...,2}... to ...,0}..., and close space between X and (\omega)
• page 114, 8th line from bottom: for upper limit of summation, change lower-case n to cap N
• page 119, line 14:  change 11/12 to 19/18
• page 119, figure 4.1: in X(\omega) column, change 4th element from bottom from 3 to 4
• page 120, 5th line of exercise 4.3c: insert comma at very end of line
• page 120, exercise 4.4c: replace "S_1, S_2, and 6" with "S_1(2) and S_2(2)"
• page 121, 8th line from bottom: change superscript of last d from t to T
• page 122, line 4 of example 4.6: change superscript of last u from 1 to i
• page 125, line 8: change Y-t to Y_t
• page 127, 2nd line of (4.6): change T = 0 to t = 0
• page 128, line 5: change (4.7) to (4.8)
• page 128, expression (4.10): change subscript of script-F from T-t to T-1
• page 128, line 10: insert an equals sign between Z_{T-1} and Y_{T-1}
• page 128, line 11: change subscript of script-F from T-t to T-1
• page 128, expression (4.11): change subscript of Y from T-1 to t-1
• page 128, expression (4.11): change subscript of script-F from t-t to t-1
• page 128, 14th line from bottom: insert minus one so it reads ...(4.9) for time t-1 we see...
• page 130, line 14: change ...states \omega_3 and \omega_4... to ...states \omega_1 and \omega_2...
• page 131, line 26: change (4.6) to (4.5)
• page 132, line 6: make left side of inequality look like (S_t/B_t - e/B_t)^+ ....
• page 132, line 8: insert a right paranthesis after the last B_{t+s}
• page 132, line 4 of exercise (4.11): insert right paranthesis just before inequality
• page 133, line 12 of section 4.4: delete "in" and insert a comma after (1.24)
• page 136, two lines from bottom: ...it follows from (3.28), not (3.22)
• page 139, line 1 of (4.27): change A_t;T= to A_t;t=
• page 140, exercise 4.14b: change B_t = 1.05 to B_1 = 1.05. Also, for parts b, c, and d provide general expressions in terms of the risk neutral probability q = Q(\omega_1,\omega_2).
• page 141, line 13 from bottom: change subscript of S from J to j
• page 142, line 5: in this display, change the subscript of B from n to t
• page 142, line 7: in this display, the terms in the sum should be written as H_n(1)S_n(1)
• page 142, line 12: on the right side of the equation, the subscript of S should be n, not 0
• page 142, display (a): it might be better to write B_0 V_T (\omega) >= V_0 B_T (\omega), all \omega
• page 142, display (b): it might be better to write B_0 V_T (\omega) > V_0 B_T (\omega), some \omega
• page 142, second line from bottom: in the display V_1 = ... , change the equals sign to greater than or equal
• page 146, line 3: delete one of the B_t factors that appears in the numerator in the middle of the display
• page 146, last line of example 4.1: close up space so it's 525/46
• page 150, 2nd line following table: change u(W) to u(w)
• page 155, line 5: change f(r,w) to f(r,\omega)
• page 161, exercise 5.6a: the superscript of w should  be -1 (so make the 1 smaller and elevated)
• page 161, exercise 5.7, line 5: insert a minus sign so u(w) = -exp(-w)
• page 162, line 1: in the numerator, change the factor [(1-q)t - (n-t)] to [(1-q)t + (n-t)]
• page 164, equation (5.16): insert a right paranthesis just before the vertical bar denoting conditional expectation
• page 168, display in exercise 5.12: the first term in the denominator on the RHS should lead off with a minus sign
• page 194, last line of table: change subscript of \omega from 4 to 5
• page 201, line 4: change epsilon to the symbol denoting \omega is an element of the set \Omega
• page 204, line 3: change (6.3) to (6.4)
• page 204, line 6: change superscript of Z from 3 to 2
• page 205, line 6: change s = 0 to s = 1
• page 205, line 9: change 0.185 to 0.8187
• page 205, column Q of table: change 0.0555 to 0.2456 and change 0.2445 to 0.0544
• page 210, line 6: change ...(n+1,t) or state (n,t)... to ...(n+1,t+1) or state (n,t+1)...
• page 210, figure 6.2: in the lower right node the subscript of r should be changed from 3 to 4
• page 211, line 12: change subscript of Z from t to tau
• page 212, line 9 from bottom: add superscripts to the three Z(0)'s, each equaling one plus the corresponding subscript
• page 214, equation 6.19: in denominator on RHS, change subscript of r from r+2 to t+2
• page 216, exercise 6.5a: start the indexing with j=t, not j=0
• page 216, exercise 6.5c: the term -1 needs to be inserted at the end of the equation (i.e., subtract one from RHS)
• page 219, line 13: change upper-case S+1 to lower-case s+1
• page 220, first line of example 6.7: change superscript of first Z from s+1 to s+i
• page 220, 4th line from bottom: change last strict inequality to equals sign
• page 221, expression (6.33): in denominator, last factor in product should be for t = \tau - 1, not t = \tau
• page 225, line 2: insert } after r_2(\omega)
• page 225, first line of displayed equation: the first term has a probability which should be conditioned on the event {\omega_1,\omega_2}, not the event {\omega_1,\omega}
• page 229, equation (6.43): change left hand side from r_t to \pi_t
• page 232, 11th line from bottom: delete the last sum of Z's
• page 232, 10th line from bottom: delete the last sum of Z's
• page 233, line 2: change 0.576 to 0.0576
• page 242, line 10: in displayed definition of Q(A), change the numerator from P(D1_A) to E[D1_A]
• page 247, third line following top display: change ...lost be restricting... to ...lost by restricting...
• page 248, two lines before (7.18): change [-1/2)^t] to [-(1/2)^t] by inserting right paranthesis
• page 248, first line after bottom display:  change ...equals 1.2. Thus... to ...equals 1/2. Thus...
• page 251, expression (A2): maximize (not minimize) the objective function Y'b
• page 252, 5 lines from bottom: set d equal to (0,...,0,-1), not (0,...,0,1)

• page 9, display (1.14): add property (c) V_0^* = 0
• page 14, second display: change EX>=1 to EX=1
• page 14, first line following second display: insert "bounded" so it reads "This is a closed, bounded, and convex..."
• page 21, 2 lines from bottom: insert a prime (to denote transpose) so it reads ...X=(X_1,...,X_K)'.
• page 26, (1.27): change subjet to subject
• page 48, display (2.31): make "solution" plural so it reads "...feasible solutions of (2.28)..."
• page 91:  change Example 3.4 to Example 3.5
• page 92, display (3.17): add property (c) V_0^* = 0
• page 94, line 10: the first \omega should have subscript 1
• page 106, line 12: T_i should be \tau_i
• page 107:  change Example 3.5 to Example 3.6
• page 109:  change Example 3.5 to Example 3.6
• page 110:  change Example 3.6 to Example 3.7
• page 111:  change X_t + i to X_t = i
• page 121, first display of Example 4.5: delete the extraneous comma
• page 122, line 3 from bottom: change "3.4" to "3.5"
• page 123, line 15 (that is, third display): just after the equality sign the symbol ")" should be replaced with the symbol "}"
• page 126, Figure 4.2: add "(here the stock pays no dividend, and the strike is 5)" to the end of the caption
• page 126, Figure 4.3: add "(here the stock pays a $1 dividend between times 1 and 2, and the strike is 4)" to the end of the caption
• page 126, Figure 4.3: bottom right rectangle should have Z_2=0, not Z_2=1
• page 130, first line following second display: change subscipt of \omega from 1 to 3
• page 130, second line following second display: change subscript of \omega from 2 to 4
• page 130, fourth line following second display: change subscript of first \omega from 3 to 1; similarly, change subscript of second \omega from 4 to 2
• page 180, first line in display for u_1(w): insert right parenthesis between } and vertical bar |
• page 196, line 4: change the subscript of the expectation operator from Q(1) to Q(2)
• page 220, 3 lines from bottom: change ...if and only if it... to ...if and only if (6.31)...
• page 222, line 8 of Section 6.4: insert "that is strictly positive" so it reads "...arbitrary probability measure that is strictly positive, although..."
• page 223, display (6.36): insert "adapted" so it reads "...if the adapted stochastic process Y..."
• page 224, bottom line:  delete the dash (hyphen) between time and tau
• page 225, 8 lines from bottom:  the 2 O's should be capitalized (and in italics)
• page 227, line 2 of Example 6.2 (continued): change "one is" to "you are"
• page 240, 13 lines from bottom: insert "V_0^* = 0" so it reads "...gains process to satisfy V_0^* = 0, G_T^*..."
• page 241, second display: replace "V_t(\omega)" by "V_{s-1}^*(\omega)"

Additional errors (and I am sure there are some!) will be posted as soon as the author (srpliska@uic.edu) is informed of their existence.