6,014 research outputs found
A general theory of intertemporal decision-making and the perception of time
Animals and humans make decisions based on their expected outcomes. Since
relevant outcomes are often delayed, perceiving delays and choosing between
earlier versus later rewards (intertemporal decision-making) is an essential
component of animal behavior. The myriad observations made in experiments
studying intertemporal decision-making and time perception have not yet been
rationalized within a single theory. Here we present a
theory-Training--Integrated Maximized Estimation of Reinforcement Rate
(TIMERR)--that explains a wide variety of behavioral observations made in
intertemporal decision-making and the perception of time. Our theory postulates
that animals make intertemporal choices to optimize expected reward rates over
a limited temporal window; this window includes a past integration interval
(over which experienced reward rate is estimated) and the expected delay to
future reward. Using this theory, we derive a mathematical expression for the
subjective representation of time. A unique contribution of our work is in
finding that the past integration interval directly determines the steepness of
temporal discounting and the nonlinearity of time perception. In so doing, our
theory provides a single framework to understand both intertemporal
decision-making and time perception.Comment: 37 pages, 4 main figures, 3 supplementary figure
Heavy tails and electricity prices
In the first years after the emergence of deregulated power markets it became apparent that for the valuation of electricity derivatives we cannot simply rely on models developed for financial or other commodity markets. However, before adequate models can be put forward the unique characteristics of electricity (spot) prices have to be thoroughly analyzed. In particular, the extreme volatility and price spikes which lead to heavy-tailed distributions of returns. In this paper we first analyze the stylized facts of electricity prices, then present two modeling approaches: jump-diffusion and regime-switching, which to some extent address the pertinent issues.Heavy-tailed distribution; Electricity spot price; Seasonality; Volatility; Price spike;
Statistical Mechanics of 2+1 Gravity From Riemann Zeta Function and Alexander Polynomial:Exact Results
In the recent publication (Journal of Geometry and Physics,33(2000)23-102) we
demonstrated that dynamics of 2+1 gravity can be described in terms of train
tracks. Train tracks were introduced by Thurston in connection with description
of dynamics of surface automorphisms. In this work we provide an example of
utilization of general formalism developed earlier. The complete exact solution
of the model problem describing equilibrium dynamics of train tracks on the
punctured torus is obtained. Being guided by similarities between the dynamics
of 2d liquid crystals and 2+1 gravity the partition function for gravity is
mapped into that for the Farey spin chain. The Farey spin chain partition
function, fortunately, is known exactly and has been thoroughly investigated
recently. Accordingly, the transition between the pseudo-Anosov and the
periodic dynamic regime (in Thurston's terminology) in the case of gravity is
being reinterpreted in terms of phase transitions in the Farey spin chain whose
partition function is just a ratio of two Riemann zeta functions. The mapping
into the spin chain is facilitated by recognition of a special role of the
Alexander polynomial for knots/links in study of dynamics of self
homeomorphisms of surfaces. At the end of paper, using some facts from the
theory of arithmetic hyperbolic 3-manifolds (initiated by Bianchi in 1892), we
develop systematic extension of the obtained results to noncompact Riemannian
surfaces of higher genus. Some of the obtained results are also useful for 3+1
gravity. In particular, using the theorem of Margulis, we provide new reasons
for the black hole existence in the Universe: black holes make our Universe
arithmetic. That is the discrete Lie groups of motion are arithmetic.Comment: 69 pages,11 figures. Journal of Geometry and Physics (in press
Statistical Mechanics of 2+1 Gravity From Riemann Zeta Function and Alexander Polynomial:Exact Results
In the recent publication (Journal of Geometry and Physics,33(2000)23-102) we
demonstrated that dynamics of 2+1 gravity can be described in terms of train
tracks. Train tracks were introduced by Thurston in connection with description
of dynamics of surface automorphisms. In this work we provide an example of
utilization of general formalism developed earlier. The complete exact solution
of the model problem describing equilibrium dynamics of train tracks on the
punctured torus is obtained. Being guided by similarities between the dynamics
of 2d liquid crystals and 2+1 gravity the partition function for gravity is
mapped into that for the Farey spin chain. The Farey spin chain partition
function, fortunately, is known exactly and has been thoroughly investigated
recently. Accordingly, the transition between the pseudo-Anosov and the
periodic dynamic regime (in Thurston's terminology) in the case of gravity is
being reinterpreted in terms of phase transitions in the Farey spin chain whose
partition function is just a ratio of two Riemann zeta functions. The mapping
into the spin chain is facilitated by recognition of a special role of the
Alexander polynomial for knots/links in study of dynamics of self
homeomorphisms of surfaces. At the end of paper, using some facts from the
theory of arithmetic hyperbolic 3-manifolds (initiated by Bianchi in 1892), we
develop systematic extension of the obtained results to noncompact Riemannian
surfaces of higher genus. Some of the obtained results are also useful for 3+1
gravity. In particular, using the theorem of Margulis, we provide new reasons
for the black hole existence in the Universe: black holes make our Universe
arithmetic. That is the discrete Lie groups of motion are arithmetic.Comment: 69 pages,11 figures. Journal of Geometry and Physics (in press
Static hedging of Asian options under Lévy models: the comonotonicity approach.
In this paper we present a simple static super-hedging strategy for the payoff of an arithmetic Asian option in terms of a portfolio of European options. Moreover, it is shown that the obtained hedge is optimal in some sense. The strategy is based on stop-loss transforms and is applicable under general stock price models. We focus on some popular Lévy models. Numerical illustrations of the hedging performance are given for various Lévy models calibrated to market data of the S&P 500.Comonotonicity; Data; Hedging; Market; Model; Models; Optimal; Options; Performance; Portfolio; Strategy;
Nonuniform Fuchsian codes for noisy channels
We develop a new transmission scheme for additive white Gaussian noisy (AWGN)
channels based on Fuchsian groups from rational quaternion algebras. The
structure of the proposed Fuchsian codes is nonlinear and nonuniform, hence
conventional decoding methods based on linearity and symmetry do not apply.
Previously, only brute force decoding methods with complexity that is linear in
the code size exist for general nonuniform codes. However, the properly
discontinuous character of the action of the Fuchsian groups on the complex
upper half-plane translates into decoding complexity that is logarithmic in the
code size via a recently introduced point reduction algorithm
Tradable Schemes
In this article we present a new approach to the numerical valuation of
derivative securities. The method is based on our previous work where we
formulated the theory of pricing in terms of tradables. The basic idea is to
fit a finite difference scheme to exact solutions of the pricing PDE. This can
be done in a very elegant way, due to the fact that in our tradable based
formulation there appear no drift terms in the PDE. We construct a mixed scheme
based on this idea and apply it to price various types of arithmetic Asian
options, as well as plain vanilla options (both european and american style) on
stocks paying known cash dividends. We find prices which are accurate to in about 10ms on a Pentium 233MHz computer and to in a
second. The scheme can also be used for market conform pricing, by fitting it
to observed option prices.Comment: 13 pages, 5 tables, LaTeX 2
- …