Arbitrage Theory in Continuous Time

By Tomas Björk. 2019

1,962 citations recorded by the source corpus.

The fourth edition of this textbook on pricing and hedging of financial derivatives, now also including dynamic equilibrium theory, continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous time arbitrage pricing of financial derivatives, including stochastic optimal control theory and optimal stopping theory, the book is designed for graduate students in economics and mathematics, and combines the necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter. All concepts and ideas are discussed, not only from a mathematics point of view, but the mathematical theory is also always supplemented with lots of intuitive economic arguments. In the substantially extended fourth edition Tomas Björk has added completely new chapters on incomplete markets, treating such topics as the Esscher transform, the minimal martingale measure, f-divergences, optimal investment theory for incomplete markets, and good deal bounds. There is also an entirely new part of the book presenting dynamic equilibrium theory. This includes several chapters on unit net supply endowments models, and the Cox–Ingersoll–Ross equilibrium factor model (including the CIR equilibrium interest rate model). Providing two full treatments of arbitrage theory—the classical delta hedging approach and the modern martingale approach—the book is written in such a way that these approaches can be studied independently of each other, thus providing the less mathematically oriented reader with a self-contained introduction to arbitrage theory and equilibrium theory, while at the same time allowing the more advanced student to see the full theory in action.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/00a475c2feb00cf03e72f8c3591fbeaadf326ff7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Finance

Citations in the corpus

Optimal investment choices post-retirement in a defined contribution pension scheme (2004, neutral): “Therefore, a minimum limit equal to at least 0 would be appropriate, as many other similar applications of HJB equation show (see, among others, the examples contained in Bj¨ork, 1998).”
STOCHASTIC HYPERBOLIC DYNAMICS FOR INFINITE‐DIMENSIONAL FORWARD RATES AND OPTION PRICING (2005, neutral): “There are many excellent books on interest rates, starting from the classical modeling of the short rate to the forward rate and including the Musiela equation, such as Bjork (1998) and Musiela and Rutkowski (1997).”
Optimal insurance in a continuous-time model (2006, methodology): “8) and Björk (1998) for the derivation of related HJB equations. There also exist verification theorems that tell us if the value function V is smooth and if V~ is a smooth solution of the associated HJB equation, then under certain regularity conditions, In those cases for which there is no smooth ”
Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans (2006, positive): “If we follow the usual steps (see, for example, Björk, 1998) we find that the optimal asset allocation strategy takes the form p∗(t, x, r; V ) = C ′−1 ( σY − (ξ − σY ) Vx xVxx − σr(r) Vxr xVxx ) .”
Mean–variance target-based optimisation for defined contribution pension schemes in a stochastic framework (2017, background): “where the new numeraire of the economy is B (t, T ) (Björk, 2009).”
The Worst Case for Real Options (2010, background): “Reference [31] points out that in the framework where the individual preferences of the decision maker are defined and the value functions consistent with these preferences are specified, the market price of risk is defined endogenously.”
Markovian Term Structure Models in Discrete Time (2002, background): “We also refer to the discussion in [1], Section 16.”
Optimal portfolios under a value-at-risk constraint (2004, methodology): “5 The optimal portfolio problem is shown to be equivalent to the problem of -nding a solution to the HJB-equation (Kamien and Schwartz, 1991; Bjork, 1998).”
Generalized Directional Gradients, Backward Stochastic Differential Equations and Mild Solutions of Semilinear Parabolic Equations (2005, background): “6, it is clear that for 2 small the above functionals are good approximations of the following general type of look-back claim (see [8], [27] or [40]):”
Randomly weighted sums of subexponential random variables with application to capital allocation (2014, background): “See, for example, Björk (2009) for discussions on stochastic discount factors. The stochastic discount factors θ1, . . . , θn should be dependent as they result from financial evolvements over the same time period. We study the tail behavior of the randomly weighted sum (1) under the assumptions tha”