Incomplete data, stochastic processes and finance

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Incomplete or missing data  and the necessity to impute missing values is a common feature of modern data in finance, economics, sample surveys, biostatistics, and other applications of statistics.  Relevant variables may be ignored either because they are difficult to obtain or  they complicate the analysis.  For example if  stock A is traded at time t, say,   another stock B is highly unlikely to be traded at exactly the same time in which case the fair value of stock B at this time is ``missing''. The usual practice of rounding the trading times up is dangerous in that it introduces biases in the estimates, possibly  of limited consequence for highly liquid equities and benchmark bonds, but much more significant  with thinly traded or illiquid assets.  Naive manufacture or ``imputation'' of data for the convenience of the data analysis runs the risk of introducing bias and undermining the original intent of the analyst; to objectively extract all pertinent information from the data. Ignoring those cases or variables which have missing components is as dangerous as naively filling in data; it too potentially leads to biased results. The objective of  my research is to make exact imputation techniques available to both multivariate and univariate diffusion models, such as those commonly used in finance, and exploit them for estimation of parameters and other problems in which interpolating the values of a diffusion is useful.    In biostatistics, there are often  response or predictor variables that  might help explain the behaviour of a ``response variable'' of interest, but they are not collected simply because of the expense of the data collection.  Similar but less precise information might be easily available from health collection agencies, hospital databases, or a simple cheap test. To what extent can the cheaper variables be used as proxies for the more expensive? Collection of the expensive  variables for even a fraction of the cases will often help assess the degree to which we sacrifice efficiency and bias when we omit these more expensive variables and usually allow for an improvement in efficiency with reduced cost.     My research concerns the "proper" imputation of data, i.e. the imputation of data using the exact distribution consistent with what we observe, so as permit use of simpler complete data techniques on these missing data problems.