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81.
The relevance-weighted likelihood function weights individual contributions to the likelihood according to their relevance
for the inferential problem of interest. Consistency and asymptotic normality of the weighted maximum likelihood estimator
were previously proved for independent sequences of random variables. We extend these results to apply to dependent sequences,
and, in so doing, provide a unified approach to a number of diverse problems in dependent data. In particular, we provide
a heretofore unknown approach for dealing with heterogeneity in adaptive designs, and unify the smoothing approach that appears
in many foundational papers for independent data. Applications are given in clinical trials, psychophysics experiments, time
series models, transition models, and nonparametric regression.
Received: April 2000 相似文献
82.
Carlos A. Ibarra 《International Review of Applied Economics》2015,29(5):716-739
The paper estimates different versions of an equation for private investment in Mexico during the post-liberalization period 1988–2013, with the aim of studying the operation of the recently discussed real exchange rate’s profitability channel. During this period, the real exchange rate (RER) was broadly positively correlated with the Mexican price/wage ratio and the Mexican/US relative profit margin in the manufacturing sector, particularly so when the RER experienced large fluctuations, before the end of disinflation in the early 2000s. In the estimations, the effect of the profit margin appears to be ‘deeper’, wiping out the effect of the RER when the two variables are included together in the investment equation. From this, the paper argues that the positive effect of the RER on investment, observed in previous studies that omitted the profit margin, reflects indirectly the positive link of the RER with the profit margin, supporting the existence of a profitability channel in Mexico. 相似文献
83.
We propose the eigenfunction expansion method for pricing options in quadratic term structure models. The eigenvalues, eigenfunctions, and adjoint functions are calculated using elements of the representation theory of Lie algebras not only in the self-adjoint case, but in non-self-adjoint case as well; the eigenfunctions and adjoint functions are expressed in terms of Hermite polynomials. We demonstrate that the method is efficient for pricing caps, floors, and swaptions, if time to maturity is 1 year or more. We also consider subordination of the same class of models, and show that in the framework of the eigenfunction expansion approach, the subordinated models are (almost) as simple as pure Gaussian models. We study the dependence of Black implied volatilities and option prices on the type of non-Gaussian innovations. 相似文献
84.
Computerised Record Linkage methods help us combine multiple data sets from different sources when a single data set with all necessary information is unavailable or when data collection on additional variables is time consuming and extremely costly. Linkage errors are inevitable in the linked data set because of the unavailability of error‐free unique identifiers. A small amount of linkage errors can lead to substantial bias and increased variability in estimating parameters of a statistical model. In this paper, we propose a unified theory for statistical analysis with linked data. Our proposed method, unlike the ones available for secondary data analysis of linked data, exploits record linkage process data as an alternative to taking a costly sample to evaluate error rates from the record linkage procedure. A jackknife method is introduced to estimate bias, covariance matrix and mean squared error of our proposed estimators. Simulation results are presented to evaluate the performance of the proposed estimators that account for linkage errors. 相似文献
85.
In this paper it is proved that the Black–Scholes implied volatility satisfies a second order non-linear partial differential equation. The obtained PDE is then used to construct an algorithm for fast and accurate polynomial approximation for Black–Scholes implied volatility that improves on the existing numerical schemes from literature, both in speed and parallelizability. We also show that the method is applicable to other problems, such as approximation of implied Bachelier volatility. 相似文献
86.
87.
In most over‐the‐counter (OTC) markets, a small number of market makers provide liquidity to other market participants. More precisely, for a list of assets, they set prices at which they agree to buy and sell. Market makers face therefore an interesting optimization problem: they need to choose bid and ask prices for making money while mitigating the risk associated with holding inventory in a volatile market. Many market‐making models have been proposed in the academic literature, most of them dealing with single‐asset market making whereas market makers are usually in charge of a long list of assets. The rare models tackling multiasset market making suffer however from the curse of dimensionality when it comes to the numerical approximation of the optimal quotes. The goal of this paper is to propose a dimensionality reduction technique to address multiasset market making by using a factor model. Moreover, we generalize existing market‐making models by the addition of an important feature: the existence of different transaction sizes and the possibility for the market makers in OTC markets to answer different prices to requests with different sizes. 相似文献
88.
The aim of this work is to advocate the use of multifractional Brownian motion (mBm) as a relevant model in financial mathematics. mBm is an extension of fractional Brownian motion where the Hurst parameter is allowed to vary in time. This enables the possibility to accommodate for varying local regularity, and to decouple it from long‐range dependence properties. While we believe that mBm is potentially useful in a variety of applications in finance, we focus here on a multifractional stochastic volatility Hull & White model that is an extension of the model studied in Comte and Renault. Using the stochastic calculus with respect to mBm developed in Lebovits and Lévy Véhel, we solve the corresponding stochastic differential equations. Since the solutions are of course not explicit, we take advantage of recently developed numerical techniques, namely functional quantization‐based cubature methods, to get accurate approximations. This allows us to test the behavior of our model (as well as the one in Comte and Renault) with respect to its parameters, and in particular its ability to explain some features of the implied volatility surface. An advantage of our model is that it is able both to fit smiles at different maturities, and to take volatility persistence into account in a more precise way than Comte and Renault. 相似文献
89.
Andrew Papanicolaou 《Mathematical Finance》2019,29(1):208-248
This paper considers a non‐Markov control problem arising in a financial market where asset returns depend on hidden factors. The problem is non‐Markov because nonlinear filtering is required to make inference on these factors, and hence the associated dynamic program effectively takes the filtering distribution as one of its state variables. This is of significant difficulty because the filtering distribution is a stochastic probability measure of infinite dimension, and therefore the dynamic program has a state that cannot be differentiated in the traditional sense. This lack of differentiability means that the problem cannot be solved using a Hamilton–Jacobi–Bellman equation. This paper will show how the problem can be analyzed and solved using backward stochastic differential equations, with a key tool being the problem's dual formulation. 相似文献
90.
Linkage errors can occur when probability‐based methods are used to link records from two distinct data sets corresponding to the same target population. Current approaches to modifying standard methods of regression analysis to allow for these errors only deal with the case of two linked data sets and assume that the linkage process is complete, that is, all records on the two data sets are linked. This study extends these ideas to accommodate the situation when more than two data sets are probabilistically linked and the linkage is incomplete. 相似文献