# Read e-book Large Deviations and Asymptotic Methods in Finance

Peter K. In he worked for Merrill Lynch, New York, before returning to academia where he then held a Readership at Cambridge University until his move to Berlin in PKF has written numerous papers in the broad area of quantitative finance, partial differential equations, stochastic analysis and two highly regarded books on applications of rough paths theory: "Multidimensional Stochastic Processes as Rough Paths" with N.

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Hairer, Springer Over his long career in the financial markets, he has been involved at one time or other in all of the major derivative product areas as book runner, risk manager and quantitative analyst. Jim has a PhD in theoretical physics from Cambridge University.

His research focus is on volatility modelling and modelling equity market microstructure for algorithmic trading.

His best-selling book, The Volatility Surface: A Practitioner's Guide Wiley , is one of the standard references on the subject of volatility modelling. Archil Gulisashvili received his Ph. In physics, the best known application of large deviations theory arise in thermodynamics and statistical mechanics in connection with relating entropy with rate function. The rate function is related to the entropy in statistical mechanics. This can be heuristically seen in the following way.

In statistical mechanics the entropy of a particular macro-state is related to the number of micro-states which corresponds to this macro-state. Loosely speaking a macro-state having a higher number of micro-states giving rise to it, has higher entropy. And a state with higher entropy has a higher chance of being realised in actual experiments. And in most practical situations we shall indeed obtain this macro-state for large numbers of trials.

The "rate function" on the other hand measures the probability of appearance of a particular macro-state.

## Option pricing in the moderate deviations regime

The smaller the rate function the higher is the chance of a macro-state appearing. In this way one can see the "rate function" as the negative of the "entropy". There is a relation between the "rate function" in large deviations theory and the Kullback—Leibler divergence see Sanov [9] and Novak, [11] ch. In a special case, large deviations are closely related to the concept of Gromov—Hausdorff limits.

From Wikipedia, the free encyclopedia.

## Large Deviations and Asymptotic Methods in Finance

Main article: asymptotic equipartition property. Varadhan, Asymptotic probability and differential equations , Comm. Pure Appl. Physics Reports. Bibcode : PhR On a new limit theorem of the theory of probability. Uspekhi Matematicheskikh Nauk, 10 , Uspehi Matem. Nauk, v.

## Large Deviations and Asymptotic Methods in Finance | SpringerLink

Sbornik, v. Large deviations techniques and applications Vol. Large deviation and the tangent cone at infinity of a crystal lattice , Math.