Stochastic processes with applications to finance. (2016)

• 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 Elements in Probability; The Sample Space and Probability; Discrete Random Variables; Continuous Random Variables; Bivariate Random Variables; Expectation; Conditional Expectation; Moment Generating Functions; Copulas Useful Distributions in Finance; Binomial Distributions; Other Discrete Distributions; Normal and Log-Normal Distributions; Other Continuous Distributions; Multivariate Normal Distributions Derivative Securities; The Money-Market Account; Various Interest Rates; Forward and Futures Contracts; Options; Interest-Rate Derivatives Change of Measures and the Pricing of Insurance Products; Change of Measures Based on Positive Random Variables ; BlackScholes Formula and Esscher Transform; Premium Principles for Insurance Products; Bühlmann’s Equilibrium Pricing Model A Discrete-Time Model for Securities Market; Price Processes; Portfolio Value and Stochastic Integral; No-Arbitrage and Replicating Portfolios; Martingales and the Asset Pricing Theorem; American Options; Change of Measures Based on Positive Martingales Random Walks; The Mathematical Definition; Transition Probabilities; The Reflection Principle; Change of Measures in Random Walks; The Binomial Securities Market Model The Binomial Model; The Single-Period Model; Multi-Period Models; The Binomial Model for American Options; The Trinomial Model; The Binomial Model for Interest-Rate Claims A Discrete-Time Model for Defaultable Securities; The Hazard Rate; Discrete Cox Processes; Pricing of Defaultable Securities ; Correlated Defaults Markov Chains; Markov and Strong Markov Properties; Transition Probabilities; Absorbing Markov Chains; Applications to Finance Monte Carlo Simulation; Mathematical Backgrounds; The Idea of Monte Carlo; Generation of Random Numbers; Some Examples from Financial Engineering; Variance Reduction Methods From Discrete to Continuous: Towards the BlackScholes; Brownian Motions; The Central Limit Theorem Revisited; The BlackScholes Formula; More on Brownian Motions; Poisson Processes Basic Stochastic Processes in Continuous Time; Diffusion Processes; Sample Paths of Brownian Motions; Continuous-Time Martingales; Stochastic Integrals; Stochastic Differential Equations; Ito;s Formula Revisited A Continuous-Time Model for Securities Market; Self-Financing Portfolio and No-Arbitrage; Price Process Models ; The BlackScholes Model; The Risk-Neutral Method; The Forward-Neutral Method Term-Structure Models and Interest-Rate Derivatives; Spot-Rate Models; The Pricing of Discount Bonds; Pricing of Interest-Rate Derivatives; Forward LIBOR and Black’s Formula A Continuous-Time Model for Defaultable Securities; The Structural Approach; The Reduced-Form Approach; Pricing of Credit Derivatives References Index Exercises appear at the end of each chapter.
• Publisher Details: Place of publication not identified : Chapman and Hall/CRC
• Publication Date: 2016
• Extent: 1 online resource, illustrations
• Subjects: 519.2; Financial engineering; Stochastic processes; Business mathematics; BUSINESS & ECONOMICS / Finance; MATHEMATICS / General; MATHEMATICS / Probability & Statistics / General
• Languages: English
• ISBNs: 9781439884843; 1439884846
• 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.