scholarly journals A GENERAL METHODOLOGY TO PRICE AND HEDGE DERIVATIVES IN INCOMPLETE MARKETS

2000 ◽  
Vol 03 (01) ◽  
pp. 1-24 ◽  
Author(s):  
ERIK AURELL ◽  
ROBERTO BAVIERA ◽  
OLA HAMMARLID ◽  
MAURIZIO SERVA ◽  
ANGELO VULPIANI
Keyword(s):  
Incomplete Markets ◽  
Large Deviation ◽  
General Situation ◽  
General Criterion ◽  
Complete Markets ◽  
Large Deviation Theory ◽  
Monte Carlo Computation ◽  
Black Scholes ◽  
Theory Approximation ◽  
Deviation Theory

We introduce and discuss a general criterion for the derivative pricing in the general situation of incomplete markets, we refer to it as the No Almost Sure Arbitrage Principle. This approach is based on the theory of optimal strategy in repeated multiplicative games originally introduced by Kelly. As particular cases we obtain the Cox–Ross–Rubinstein and Black–Scholes in the complete markets case and the Schweizer and Bouchaud–Sornette as a quadratic approximation of our prescription. Technical and numerical aspects for the practical option pricing, as large deviation theory approximation and Monte Carlo computation are discussed in detail.

Large deviations in the supercritical branching process

1993 ◽  
Vol 25 (04) ◽  
pp. 757-772 ◽  
Author(s):  
J. D. Biggins ◽  
N. H. Bingham
Keyword(s):  
Distribution Function ◽  
Large Deviations ◽  
Population Size ◽  
Branching Process ◽  
Large Deviation ◽  
Moment Generating Function ◽  
Large Deviation Theory ◽  
Tail Behaviour ◽  
The Moment ◽  
Deviation Theory

The tail behaviour of the limit of the normalized population size in the simple supercritical branching process, W, is studied. Most of the results concern those cases when a tail of the distribution function of W decays exponentially quickly. In essence, knowledge of the behaviour of transforms can be combined with some ‘large-deviation' theory to get detailed information on the oscillation of the distribution function of W near zero or at infinity. In particular we show how an old result of Harris (1948) on the asymptotics of the moment-generating function of W translates to tail behaviour.

ON LOGARITHMIC ASYMPTOTICS OF STOCHASTIC RESONANCE FREQUENCIES

2003 ◽  
Vol 03 (01) ◽  
pp. 55-71
Author(s):  
S. C. CARMONA ◽  
M. I. FREIDLIN
Keyword(s):  
Dynamical Systems ◽  
Stochastic Resonance ◽  
Small Amplitude ◽  
Large Deviation ◽  
Large Deviation Theory ◽  
Resonance Effects ◽  
Resonance Frequencies ◽  
Logarithmic Asymptotics ◽  
The Relationship ◽  
Deviation Theory

Stochastic resonance effects due to arbitrarily small amplitude deterministic perturbations in dynamical systems with noise are studied. The concept of Log-Asymptotic Resonance Frequency is introduced and the relationship between its existence and some types of symmetries in the stochastic system is established; the spectrum of this kind of frequencies is determined. These symmetries are defined through the quasi-deterministic approximation of the system. The large deviation theory gives the basic machinery for this analysis.

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