Financial Markets in Continuous Time

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Springer Science & Business Media, Jul 12, 2007 - Business & Economics - 326 pages
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In modern financial practice, asset prices are modelled by means of stochastic processes, and continuous-time stochastic calculus thus plays a central role in financial modelling. This approach has its roots in the foundational work of the Nobel laureates Black, Scholes and Merton. Asset prices are further assumed to be rationalizable, that is, determined by equality of demand and supply on some market. This approach has its roots in the foundational work on General Equilibrium of the Nobel laureates Arrow and Debreu and in the work of McKenzie. This book has four parts. The first brings together a number of results from discrete-time models. The second develops stochastic continuous-time models for the valuation of financial assets (the Black-Scholes formula and its extensions), for optimal portfolio and consumption choice, and for obtaining the yield curve and pricing interest rate products. The third part recalls some concepts and results of general equilibrium theory, and applies this in financial markets. The last part is more advanced and tackles market incompleteness and the valuation of exotic options in a complete market.
 

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Contents

Contents
1
Dynamic Models in Discrete Time 43
42
The BlackScholes Formula
81
Portfolios Optimizing Wealth and Consumption 127
126
The Yield Curve
159
Equilibrium of Financial Markets in Discrete Time
191
Equilibrium of Financial Markets in Continuous Time
216
Incomplete Markets
237
2
245
3
252
A Brownian Motion
279
B Numerical Methods
287
References
301
Incomplete Markets 8 1 1 The Case of Constant Coefficients 8 1 2 NoArbitrage Markets 8 1 3 The Price Range 8 1 4 Superhedging 8 1 5 The Minim...
313
Index 323
322
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