Fractional Brownian motion inference of multivariate stochastic differential equations

Recently, the financial mathematics has been emerged to interpret and predict the underlying mechanism that generates an incident of concern. A system of differential equations can reveal a dynamical development of financial mechanism across time. Multivariate wiener process represents the stochastic term in a system of stochastic differential equations (SDE). The standard wiener process follows a Markov chain, and hence it is a martingale (kind of Markov chain), which is a good integrator. Though, the fractional Wiener process does not follow a Markov chain, hence it is not a good integrator. This problem will produce an Arbitrage (non-equilibrium in the market) in the predicted series. It is undesired property that leads to erroneous conclusion, as it is not possible to build a mathematical model, which represents the financial phenomenon. If there is Arbitrage (unbalance) in the market, this can be solved by Wick-Itô-Skorohod stochastic integral (renormalized integral). This paper considers the estimation of a system of fractional stochastic differential equations (FSDE) using maximum likelihood method, although it is time consuming. However, it provides estimates with desirable characteristic with the most important consistency. Langevin method can be used to find the mathematical form of the functions of stochastic differential equations. This includes drift and diffusion by estimating conditional mean and variance from the data and finding the suitable function achieves the least error, and then estimating the parameters of the model by numerical optimal solution search method. Data used in this paper consist of three banking sector stock prices including Baghdad Bank (BBOB), the Commercial Bank (BCOI), and the National Bank (BNOI)

Validation of the diabetes, hypertension and hyperlipidemia (DHL) knowledge instrument in Malaysia

BACKGROUND: Patient's knowledge on diabetes, hypertension and hyperlipidaemia and its medications can be used as one of the outcome measures to assess the effectiveness of educational intervention. To date, no such instrument has been validated in Malaysia. Therefore, the aim of this study was to evaluate the validity and reliability of the Diabetes, Hypertension and Hyperlipidemia (DHL) knowledge instrument for assessing the knowledge of patients with type 2 diabetes in Malaysia. METHODS: A 28-item instrument which comprised of 5 domains: diabetes, hypertension, hyperlipidemia, medications and general issues was designed and tested. One point was given for every correct answer, whilst zero was given for incorrect answers. Scores ranged from 0 to 28, which were then converted into percentage. This was administered to 77 patients with type 2 diabetes in a tertiary hospital, who were on medication(s) for diabetes and who could understand English (patient group), and to 40 pharmacists (professional group). The DHL knowledge instrument was administered again to the patient group after one month. Excluded were patients less than 18 years old. RESULTS: Flesch reading ease was 60, which is satisfactory, while the mean difficulty factor(SD) was 0.74(0.21), indicating that DHL knowledge instrument was moderately easy. Internal consistency of the instrument was good, with Cronbach's alpha = 0.791. The test-retest scores showed no significant difference for 26 out of the 28 items, indicating that the questionnaire has achieved stable reliability. The overall mean(SD) knowledge scores was significantly different between the patient and professional groups 74.35(14.88) versus 93.84(6.47), p < 0.001. This means that the DHL knowledge instrument could differentiate the knowledge levels of participants. The DHL knowledge instrument shows similar psychometric properties as other validated questionnaires. CONCLUSIONS: The DHL knowledge instrument shows good promise to be adopted as an instrument for assessing diabetic patients' knowledge concerning their disease conditions and medications in Malaysia

Comparison of three medication adherence measures in patients taking warfarin

10.1007/s11239-013-0872-5Journal of Thrombosis and Thrombolysis364416-421JTTH