Stochastic processes with applications to finance. (2002)

• Record Type: Book
• Further Information: Note: Masaaki Kijima.
• Other Names: Kijima, Masaaki, 1957-
• Contents: ELEMENTARY CALCULUS: TOWARDS ITO'S FORMULA; Exponential and Logarithmic Functions; Differentiation; Taylor's Expansion; Ito's Formula; Integration; Exercises; ELEMENTS IN PROBABILITY; The Sample Space and Probability; Discrete Random Variables; Continuous Random Variables; Multivariate Random Variables; Expectation; Conditional Expectation; Moment Generating Functions; Exercises; USEFUL DISTRIBUTIONS IN FINANCE; Binomial Distributions; Other Discrete Distribution; Normal and Log-Normal Distributions; Other Continuous Distributions; Multivariate Normal Distributions; Exercises; DERIVATIVE SECURITIES; The Money-Market Account; Various Interest Rates; Forward and Futures Contracts; Options; Interest-Rate Derivatives; Exercises; A DISCRETE-TIME MODEL FOR SECURITIES MARKET; Price Processes; The Portfolio Value and Stochastic Integral; No-Arbitrage and Replication Portfolios; Martingales and the Asset Pricing Theorem; American Options; Change of Measure; Exercises; RANDOM WALKS; The Mathematical Definition; Transition Probabilities; The Reflection Principle; Change of Measure Revisited; A Binomial Securities Market Model; Exercises; THE BINOMIAL MODEL; The Single-Period Model; The Multi-Period Model; The Binomial Model for American Options; The Trinomial Model; The Binomial Model for Interest-Rate Claims; Exercises; A DISCRETE-TIME MODEL FOR DEFAULTABLE SECURITIES; The Hazard Rate; A Discrete Hazard Model; Pricing of Defaultable Securities; Correlated Defaults; Exercises; MARKOV CHAINS; Markov and Strong Markov Properties; Transition Probabilities; Absorbing Markov Chains; Applications to Finance; Exercises; THE MONTE CARLO SIMULATION; Mathematical Backgrounds; The Idea of Monte Carlo; Generation of Random Numbers; Some Examples for Financial Engineering; Variance Reduction Methods; Exercises; FROM DISCRETE TO CONTINUOUS: TOWARDS THE BLACK-SCHOLES; Brownian Motions; The Central Limit Theorem Revisited; The Black-Scholes Formula; More on Brownian Motions; Poisson Processes; Exercises; BASIC STOCHASTIC PROCESSES IN CONTINUOUS TIME; Diffusion Processes; Sample Paths of Brownian Motions; Martingales; Stochastic Integrals; Stochastic Differential Equations; Ito's Formula Revisited; Exercises; A CONTINUOUS-TIME MODEL FOR SECURITIES MARKET; Self-Financing Portfolio and No-Arbitrage; Price Process Models; The Black-Scholes Model; The Risk-Neutral Method; The Forward-Neutral Method; The Interest-Rate Term Structure; Pricing of Interest-Rate Derivatives; Pricing of Corporate Debts; Exercises; REFERENCES
• Publisher Details: Place of publication not identified : Chapman and Hall/CRC
• Publication Date: 2002
• Extent: 1 online resource (288 pages), (31 illustrations)
• Subjects: 519.2; Stochastic processes; Business mathematics
• Languages: English
• ISBNs: 9781420057607
• Related ISBNs: 142005760X
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.