# conditional expectation

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## conditional expectation

[kən′dish·ən·əl ‚ek‚spek′tā·shən]
(mathematics)
If X is a random variable on a probability space (Ω, F,P), the conditional expectation of X with respect to a given sub σ-field F′ of F is an F′-measurable random variable whose expected value over any set in F′ is equal to the expected value of X over this set.
(statistics)
The expected value of a conditional distribution.
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Although I may not subscribe to Jarocinski and Smets's interpretation of the conditional expectation of output or inflation as an indicator of monetary conditions, I do agree with their conclusion that housing is at the core of the business cycle, so it should have a prominent role in the formulation of monetary policy.
Given a realisation of a spatio-temporal point process X of spikes and given a trajectory of the path Y, the solution of the nonlinear filtering problem is the conditional expectation E[[LAMBDA]|X,Y] which is not explicitly available.
The new releases include Tail Conditional Expectation (TCE) as an additional Probable Maximum Loss (PML) metric to analyze account and portfolio risk.
21] as the derivative of the conditional expectation in (9), evaluated at the mean of [x.
If the loss is proportional to the square of the forecast error then we have a quadratic loss function and the forecast which minimises the expected loss is the conditional expectation or mean of the forecast density.
The conclusion, drawn from the existing literature, is that while there is no generally accepted model of the stochastic discount factor, its conditional expectation must be relatively stable in order to explain the stability of the riskless real interest rate.
The analytical tools for measuring the economic value associated with the exercise of the intellectual property right in a foreign nation are the conditional expectation of marginal revenues and the conditional expectation of marginal costs.
Hasbrouck shows that the short-term movements of a security price reflect the latent efficient price (or, the conditional expectation of terminal value) and various components arising from the trading mechanism itself.
He covers the basic financial instruments; fundamental principles of financial modeling and arbitrage valuation of derivatives; the concept of conditional expectation, the discrete time binomial model and its application to stochastic finance; the most important results from the theory of martingales in the theory and application of stochastic finance; more advanced concepts such as the Randon-Nikodym derivative, equivalent martingale measure, non-arbitrage, and complete general markets; American derivative securities using the binomial model and general markets; fixed-income markets and the interest rate theory in discrete time; arbitrage pricing; credit risk; and the Heath-Jarrow-Morton model for the evolution of forward rate process.
He covers money and markets (including interest rates) fair games (including hedging and arbitrage), set theory, measurable functions (including the Borel field), probability spaces (including random variables and stochastic processes) expected values, continuity and integrability, conditional expectation, martingales (discrete, continuous, and in convergence), the Black- Scholes formula itself, and stochastic integration.
Best will be requesting Tail Value at Risk (TVAR) or Tail Conditional Expectation (TCE) for the various return periods.

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