## Arbitrage Theory in Continuous TimeProfessor Bjork provides an accessible introduction to the classical underpinnings of the central mathematical theory behind modern finance. Combining sound mathematical principles with the necessary economic focus, Arbitrage Theory in Continuous Time is specifically designed for graduate students, and includes solved examples for every new technique presented, numerous exercises, and Further Reading lists for each chapter. - ;The second edition of this popular introduction to the classical underpinnings of the mathematics behind finance continues to combine sound mathematical principles with. |

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### Contents

1 Introduction | 1 |

2 The Binomial Model | 6 |

3 Stochastic Integrals | 27 |

4 Differential Equations | 52 |

5 Portfolio Dynamics | 69 |

6 Arbitrage Pricing | 76 |

7 Completeness and Hedging | 99 |

8 Parity Relations and Delta Hedging | 108 |

13 Barrier Options | 182 |

14 Stochastic Optimal Control | 198 |

15 Bonds and Interest Rates | 228 |

16 Short Rate Models | 242 |

17 Martingale Models for the Short Rate | 252 |

18 Forward Rate Models | 266 |

19 Change of Numeraire | 274 |

20 Forwards and Futures | 297 |

9 Several Underlying Assets | 119 |

10 Incomplete Markets | 135 |

11 Dividends | 154 |

12 Currency Derivatives | 167 |

303 | |

308 | |

### Common terms and phrases

absence of arbitrage arbitrage free price arbitrage possibilities assume Assumption Black–Scholes model bond prices consider contingent claim contract function control law currency defined definition denote derivative dividend European call option Exercise expected value fact fixed forward contract forward rate futures contract geometric Brownian motion gives hedging HJB equation Hull-White model interest rate interval Itô formula Lemma linear market price martingale measure matrix maturity measure Q notation numeraire obtain portfolio h price dynamics price of risk pricing equation pricing formula pricing function Proof Proposition Q-dynamics rate of interest rate of return replicating portfolio risk free asset risk neutral valuation self-financing portfolio short rate solution solve standard Black–Scholes stochastic differential stochastic integral stochastic process stock price strike price T-claim term structure Theorem traded asset underlying asset underlying stock value process volatility Wiener process zero coupon bonds