Estimation and Hypothesis Testing for Stochastic Differential Equations with Time-Dependent Parameters

There are two sources of information available in empirical research in finance: one corresponding to historical data and the other to prices currently observed in the markets. When proposing a model, it is desirable to use information from both sources. However in modern finance, where stochastic differential equations have been one of the main modeling tools, the common models are typically different for historical data and for current market data. The former are usually assumed to be time homogeneous, while the latter are typically time in-homogeneous. This practice can be explained by the fact that a time-homogeneous model is stationary and easier to estimate, while time-inhomogeneous model are required in order to replicate market data sufficiently well without creating arbitrage opportunities. In this thesis, we study methods of statistical inference, both parametric and non-parametric, for stochastic differential equations with time-dependent parameters. In the first part, we propose a new class of stochastic differential equation with time-dependent drift and diffusion terms, where some of the parameters change according to a hidden Markov process. We show that under some technical conditions this innovative way of modeling switching times renders the resulting model stationary. We also explore different approaches to estimate parameters in our proposed model. Our simulation studies demonstrate that the parameters of the model can be efficiently estimated by using a version of the filtering method proposed in the literature. We illustrate our model and the proposed estimation method by applying them to interest rate data, and we detect significant time variations in early 1980s, when targets of the monetary policy in the United States were changed. One of the known drawbacks of parametric models is the risk of model misspecification. In the second part of the thesis, we allow the drift to be time-dependent and nonparametric, and our objective is to estimate it using a single trajectory of the process. The main idea underlying this method is to approximate the time-dependent function with a sequence of polynomials. Since we can estimate efficiently only a finite number of parameters for any finite length of data, in our method we propose to relate the number of parameters to the length of the observed trajectory. This idea is similar to the method of sieves proposed by Grenander (Abstract Inference, 1981). The asymptotic analysis that we present is based on the assumption that the length of available data $T$ increases to infinity. We investigate two cases, one is a Brownian motion with time-dependent drift and the other corresponds to a class of mean-reverting stochastic differential equations with time-dependent mean-reversion level. In both cases we prove asymptotic consistency and normality of a modified maximum likelihood estimator of the projected time-dependent component. The main challenge in proving our results in the second case stems from two features of the problem: one is due to the fact that coefficients of projections change with $T$ and the other is related to the confounding effect between the mean-reversion speed and the level function. By applying our method to the same interest rate data we use in the first part, we find another evidence of time-variation in the drift term

Regulation of Aldo–Keto Reductases in Human Diseases

The aldo–keto reductases (AKRs) are a superfamily of NAD(P)H-linked oxidoreductases, which reduce aldehydes and ketones to their respective primary and secondary alcohols. AKR enzymes are increasingly being recognized to play an important role in the transformation and detoxification of aldehydes and ketones generated during drug detoxification and xenobiotic metabolism. Many transcription factors have been identified to regulate the expression of human AKR genes, which could have profound effects on the metabolism of endogenous mediators and detoxication of chemical carcinogens. This review summarizes the current knowledge on AKR regulation by transcription factors and other mediators in human diseases

FXR signaling in metabolic disease

AbstractFarnesoid X receptor (FXR), a member of the nuclear receptor superfamily, has been shown to be important in controlling numerous metabolic pathways; these include roles in maintaining bile acid, lipid and glucose homeostasis, in preventing intestinal bacterial infection and gallstone formation and in modulating liver regeneration and tumorigenesis. The accumulating data suggest that FXR may be a pharmaceutical target for the treatment of certain metabolic diseases

SREBP-1 integrates the actions of thyroid hormone, insulin, cAMP, and medium-chain fatty acids on ACCalpha transcription in hepatocytes

In chick embryo hepatocytes, activation of acetyl-CoA carboxylase-α (ACCα) transcription by 3,5,3′-triiodothyronine (T3) is mediated by a cis-acting regulatory unit (−101 to −71 bp) that binds the nuclear T3 receptor (TR) and sterol regulatory element-binding protein-1 (SREBP-1). SREBP-1 directly interacts with TR on the ACCα gene to enhance T3-induced transcription. Here, we show that treating hepatocytes with T3 or insulin stimulates a 4-fold increase in the concentration of the mature, active form of SREBP-1. When T3 and insulin are added together, a 7-fold increase in the mature SREBP-1 concentration is observed. Time course studies indicate that the T3-induced increase in mature SREBP-1 abundance is closely associated with changes in ACCα transcription and that the mechanism mediating the effect of T3 on mature SREBP-1 is distinct from that mediating the effect of insulin. Transfection analyses indicate that inhibition of ACCα transcription by cAMP or hexanoate is mediated by ACCα sequences between −101 and −71 bp. Treatment with cAMP or hexanoate suppresses the increase in mature SREBP-1 abundance caused by T3 and insulin. These results establish a new interaction between the SREBP-1 and TR signaling pathways and provide evidence that SREBP-1 plays an active role in mediating the effects of T3, insulin, cAMP, and hexanoate on ACCα transcription

Hepatic Carboxylesterase 1 Is Induced by Glucose and Regulates Postprandial Glucose Levels

Metabolic syndrome, characterized by obesity, hyperglycemia, dyslipidemia and hypertension, increases the risks for cardiovascular disease, diabetes and stroke. Carboxylesterase 1 (CES1) is an enzyme that hydrolyzes triglycerides and cholesterol esters, and is important for lipid metabolism. Our previous data show that over-expression of mouse hepatic CES1 lowers plasma glucose levels and improves insulin sensitivity in diabetic ob/ob mice. In the present study, we determined the physiological role of hepatic CES1 in glucose homeostasis. Hepatic CES1 expression was reduced by fasting but increased in diabetic mice. Treatment of mice with glucose induced hepatic CES1 expression. Consistent with the in vivo study, glucose stimulated CES1 promoter activity and increased acetylation of histone 3 and histone 4 in the CES1 chromatin. Knockdown of ATP-citrate lyase (ACL), an enzyme that regulates histone acetylation, abolished glucose-mediated histone acetylation in the CES1 chromatin and glucose-induced hepatic CES1 expression. Finally, knockdown of hepatic CES1 significantly increased postprandial blood glucose levels. In conclusion, the present study uncovers a novel glucose-CES1-glucose pathway which may play an important role in regulating postprandial blood glucose levels