Citation: Mungrue Kameel, Sankar Steven, Kamalodeen Aleem, Lalchansingh Dayna, Ramnarace Demeytri, Samodee Shanala, Sookhan Craig, Sookar Navin, Sooknanan Kristal, St.George Leah, Suruj Deonath. Evaluation and Use of Registry Data in a GIS Analysis of Diabetes[J]. AIMS Public Health, 2015, 2(3): 318-331. doi: 10.3934/publichealth.2015.3.318
| [1] | Nur Ezyanie Safie, Mohd Asyadi Azam . Understanding the structural properties of feasible chemically reduced graphene. AIMS Materials Science, 2022, 9(4): 617-627. doi: 10.3934/matersci.2022037 |
| [2] | Antonina M. Monaco, Anastasiya Moskalyuk, Jaroslaw Motylewski, Farnoosh Vahidpour, Andrew M. H. Ng, Kian Ping Loh, Milos Nesládek, Michele Giugliano . Coupling (reduced) Graphene Oxide to Mammalian Primary Cortical Neurons In Vitro. AIMS Materials Science, 2015, 2(3): 217-229. doi: 10.3934/matersci.2015.3.217 |
| [3] | Derek Michael Forrester, Hsuan-Hsiou Forrester . Rapid reproduction of complex images in graphite by laser etching and exfoliation. AIMS Materials Science, 2017, 4(2): 413-420. doi: 10.3934/matersci.2017.2.413 |
| [4] | Haiqing Yao, Fei Li, Jodie Lutkenhaus, Masaya Kotaki, Hung-Jue Sue . High-performance photocatalyst based on nanosized ZnO-reduced graphene oxide hybrid for removal of Rhodamine B under visible light irradiation. AIMS Materials Science, 2016, 3(4): 1410-1425. doi: 10.3934/matersci.2016.4.1410 |
| [5] | Christoph Janiak . Inorganic materials synthesis in ionic liquids. AIMS Materials Science, 2014, 1(1): 41-44. doi: 10.3934/matersci.2014.1.41 |
| [6] | Maocong Hu, Zhenhua Yao, Xianqin Wang . Characterization techniques for graphene-based materials in catalysis. AIMS Materials Science, 2017, 4(3): 755-788. doi: 10.3934/matersci.2017.3.755 |
| [7] | Sekhar Chandra Ray . Possible magnetic performances of graphene-oxide and it's composites: A brief review. AIMS Materials Science, 2023, 10(5): 767-818. doi: 10.3934/matersci.2023043 |
| [8] | J Sharath Kumar, Naresh Chandra Murmu, Tapas Kuila . Recent trends in the graphene-based sensors for the detection of hydrogen peroxide. AIMS Materials Science, 2018, 5(3): 422-466. doi: 10.3934/matersci.2018.3.422 |
| [9] | Mohamed Jaffer Sadiq Mohamed, Denthaje Krishna Bhat . Novel ZnWO4/RGO nanocomposite as high performance photocatalyst. AIMS Materials Science, 2017, 4(1): 158-171. doi: 10.3934/matersci.2017.1.158 |
| [10] | Dinesh Rangappa, Erabhoina Hari Mohan, Varma Siddhartha, Raghavan Gopalan, Tata Narasinga Rao . Preparation of LiMn2O4 Graphene Hybrid Nanostructure by Combustion Synthesis and Their Electrochemical Properties. AIMS Materials Science, 2014, 1(4): 174-183. doi: 10.3934/matersci.2014.4.174 |
For modeling of fluctuations in movement of underlying asset price, Brownian motion has been used traditionally as the driving force [1]. However, based on some empirical studies it has been shown that financial data exhibiting periods of constant values which this property can not represent by Brownian motion [2]. In recent years, many researchers attempt to fix this gap by using subdiffusive Brownian motion. Magdziarz [3] introduced subdiffusive geometric Brownian motion as the model of underlying asset price, and obtained the corresponding subdiffusive Black-Scholes (BS) formula for the fair price of European options. Liang et al. [4] extended the model of [3] into a fractional regime. Based on the fractional Fokker-Planck equation, they obtained the corresponding BS formula for European options. Wang et al. [5] considered the European option pricing in subdiffusive fractional Brownian motion regime with transaction costs. They obtained the pricing formula for European options in continuous time. One can refer to [6,7,8,9] to see more about the option pricing model in subdiffusive regime.
Asian options are financial derivatives whose payoff depends on the average of the prices of the underlying asset over a pre-fixed time interval. We will denote by $ \{S_{t}\}_{t\in [0, T]} $ the risky asset price process. According to the payoffs on the expiration date, Asian options can be differentiated in to two classes: fixed strike price Asian options and floating strike price Asian options. The payoff for a fixed strike price Asian option is $ (J_{T}-K)^{+} $ and $ (K-J_{T})^{+} $ for a call and put option respectively. The payoff for a floating strike price Asian option is $ (S_{T}-J_{T})^{+} $ and $ (J_{T}-S_{T})^{+} $ for a call and put option respectively. Where $ T $ is the expiration date, $ K $ is the strike price, $ J_{t} $ is the average price of the underlying asset over the predetermined interval. According to the definition of $ J_{t} $, Asian options can again be divided into two types: the arithmetic average Asian option, where
|
$ Jt=1t∫t0Sτdτ, $
|
and the geometric average Asian option, where
|
$ Jt=exp{1t∫t0lnSτdτ}. $
|
(1.1) |
In recent years, scholars considered Asian option pricing under different models. Prakasa Rao [10] studied pricing model for geometric Asian power options under mixed fractional Brownian motion regime. They derived the pricing formula for European option when Hurst index $ H > \frac{3}{4} $. Mao and Liang [11] discussed geometric Asian option under fractional Brownian motion framework. They derived a closed form solution for geometric Asian option. Zhang et al.[12] evaluated geometric Asian power option under fractional Brownian motion frame work.
To the best of our knowledge, pricing of geometric Asian option under subdiffusive regime has not been considered before. The main purpose of this paper is to evaluate the price of Asian power option under a subdiffusive regime.
The rest of the paper proceeds as follows: In section 2, the concept of subdiffusive Brownian motion and basic characteristics of inverse $ \alpha- $stable subordinator are introduced. In section 3, the subdiffusive partial differential equations for geometric Asian option and the explicit formula for geometric Asian option are derived. In section 4, some numerical results are given.
Let $ B(t) $ is a standard Brownian motion, then $ B(T_{\alpha}(t)) $ is called a subdiffusive Brownian motion. Where $ T_{\alpha}(t) $ is the inverse $ \alpha $-stable subordinator defined as below
|
$ Tα(t)=inf{τ>0:Uα(τ)>t}, $
|
(2.1) |
here $ U_{\alpha}(\tau)_{\tau\geq0} $ is a strictly increasing $ \alpha $-stable L$ \acute{e} $vy process [13,14] with Laplace transform: $ \mathbb{E}(e^{-uU_{\alpha}(\tau)}) = e^{-\tau u^{\alpha}} $, $ \alpha \in (0, 1) $. $ U_{\alpha}(t) $ is $ \frac{1}{\alpha} $-self-similar $ T_{\alpha}(t) $ is $ \alpha $-self-similar, that is for every $ c > 0 $, $ U_{\alpha}(ct)\overset{\text{d}}{ = }c^{\frac{1}{\alpha}}U_{\alpha}(t) $, $ T_{\alpha}(ct)\overset{\text{d}}{ = }c^{\alpha}T_{\alpha}(t) $, where$ \overset{\text{d}}{ = } $ denotes "is identical in law to". The moments of the considered process can be found in [15]
|
$ E[Tnα(t)]=tnαn!Γ(nα+1), $
|
where $ \Gamma(\cdot) $ is the gamma function. Moreover, the Laplace transform of $ T_{\alpha}(t) $ equals
|
$ E(e−uTα(t))=Eα(−utα), $
|
where the function $ E_{\alpha}(z) = \sum_{n = 0}^{\infty}\frac{z^n}{\Gamma(n\alpha+1)} $ is the Mittag-Leffler function[16]. Specially, when $ \alpha $ $ \uparrow 1 $, $ T_{\alpha}(t) $ reduces to the "objective time" $ t $.
In this section, under the framework of PDE method and delta-hedging strategy, we will discuss the pricing problem of the geometric Asian call options in a subdiffusive environment.
Consider a subdiffusive version of the Black-Scholes model, i.e., a simple financial market model consists of a risk-less bond and a stock, whose price dynamics are respectively given by
|
$ dQt=rQtdt,Q(0)=Q0, $
|
(3.1) |
with constant interest rate $ r > 0 $. The stock price $ S_{t} = {X}\left(T_{\alpha}(t)\right) $, in which $ {X}(\tau) $ follows
|
$ dX(τ)=μX(τ)dτ+σX(τ)dB(τ),X(0)=S0, $
|
(3.2) |
where $ \mu $, $ \sigma $ are constants.
In addition, we assume that the following assumptions holds:
(ⅰ) There are no transaction costs, margin requirements, and taxes; all securities are perfectly divisible; there are no penalties to short selling; the stock pays no dividends or other distributions; and all investors can borrow or lend at the same short rate.
(ⅱ) The option can be exercised only at the time of maturity.
The value of a geometric average Asian call option at time t is function of time and of $ S_{t} $ and $ J_{t} $, that is, $ V_{t} = V(t, S_{t}, J_{t}) $, where $ V(t, S, J) $ is a measurable function of $ (t, S, J)\in[0, T]\times (0, +\infty)\times (0, +\infty) $. Then we can obtain the following result.
Theorem 3.1. Suppose the stock price $ S $ follows the model given by Eq (3.2), the price of the geometric average Asian call option $ V(t, S, J) $ satisfies the following PDE.
|
$ ∂V∂t+12σ2tα−1Γ(α)S2∂2V∂S2+JlnS−lnJt∂V∂J+rS∂V∂S−rV=0, $
|
(3.3) |
with the terminal condition
|
$ V(T,S,J)={(J−K)+,fixedstrikeAsiancalloption,(S−J)+,floatingstrikeAsiancalloption, $
|
(3.4) |
where $ \{0 < t < T, 0 < S < \infty, 0 < J < \infty \} $.
Proof of Theorem 3.1
Consider a replicating portfolio $ \Pi $ consists with one unit option $ V_{t} = V(t, S_{t}, J_{t}) $ and $ \Delta $ units of stock. At time $ t $ the value of this portfolio is
|
$ Π=V−ΔS, $
|
where to simplify the notation we omit $ t $.
Suppose that $ \Delta $ does not change over the time interval $ (t, t+dt) $, then we will select appropriate $ \Delta $ and make $ \Pi $ is risk-free over the time interval $ (t, t+dt) $.
It follows from [5] that the differential of portfolio $ \Pi $ can be expressed as
|
$ dΠ=dV−ΔdS=(∂V∂t+12σ2tα−1Γ(α)S2∂2V∂S2)dt+∂V∂SdS+∂V∂JdJ−ΔdS=(∂V∂t+12σ2tα−1Γ(α)S2∂2V∂S2+∂V∂JdJdt)dt+(∂V∂S−Δ)dS $
|
(3.5) |
Letting $ \Delta = \frac{\partial V}{\partial S} $, as
|
$ dΠ=rΠdt=r(V−ΔS)dt, $
|
then we can obtain
|
$ ∂V∂t+12σ2tα−1Γ(α)S2∂2V∂S2+∂V∂JdJdt+rS∂V∂S−rV=0. $
|
(3.6) |
From Eq (1.1) we know
|
$ dJdt=J[lnS−lnJt]. $
|
(3.7) |
Substituting Eq (3.7) into Eq (3.6) we have
|
$ ∂V∂t+12σ2tα−1Γ(α)S2∂2V∂S2+JlnS−lnJt∂V∂J+rS∂V∂S−rV=0. $
|
(3.8) |
This equation is written on the pair $ (S_{t}, J_{t}) $, but since it has a continuous distribution with support on $ (0, +\infty)\times (0, +\infty) $, it follows that the function $ V(t, S, J) $ solves the PDE (3.3) and this completes the proof.
Proof is completed.
Solving the terminal value problem of partial differential Eqs (3.3) and (3.4), we can obtain
Theorem 3.2. If the stock price $ S $ follows the model given by Eq (3.2), then the price of a fixed strike geometric average Asian call option $ V(t, S, J) $ is given by
|
$ V(t,S,J)=(JtS(T−t))1Teδ(t)+σ22(a∗+b∗)−r(T−t)Φ(d1)−Ke−r(T−t)Φ(d2), $
|
(3.9) |
where the function $ \Phi(x) $ is the cumulative probability function for a standard normal distribution and
|
$ d1=ln(Jt/TS(T−t)/TK)+δ(t)+σ2(a∗+b∗)σ√a∗+b∗, $
|
|
$ d2=d1−σ√a∗+b∗, $
|
|
$ a∗=(Tα−tα)αΓ(α)−2T(α+1)Γ(α)(Tα+1−tα+1), $
|
|
$ b∗=1T2(α+2)Γ(α)(Tα+2−tα+2). $
|
|
$ δ(t)=r2T(T−t)2−σ22αΓ(α)(Tα−tα)+σ22T(α+1)Γ(α)(Tα+1−tα+1). $
|
Proof of theorem 3.2
We make the same transformation of variables as [12]
|
$ ξ=tlnJ+(T−t)lnST, $
|
(3.10) |
and
|
$ V(t,S,J)=U(t,ξ). $
|
(3.11) |
Though calculating we can get the following Cauchy problem
|
$ {∂U∂t+12σ2tα−1Γ(α)(T−tT)2∂2U∂ξ2+[r−12σ2tα−1Γ(α)]T−tT∂U∂ξ−rU=0,U(T,ξ)=(eξ−K)+. $
|
(3.12) |
Furthermore, we apply the following transformation of variables
|
$ W=Ueβ(t), $
|
(3.13) |
|
$ η=ξ+δ(t), $
|
(3.14) |
|
$ τ=γ(t). $
|
(3.15) |
Substituting Eqs (3.13) and (3.15) into Eq (3.12) we can obtain
|
$ γ′(t)∂W∂τ+12σ2tα−1Γ(α)(T−tT)2∂2W∂η2+[(r−12σ2tα−1Γ(α))T−tT+δ′(t)]∂W∂η−(r+β′(t))W=0, $
|
Letting
|
$ r+β′(t)=0, $
|
|
$ (r−12σ2tα−1Γ(α))T−tT+δ′(t)=0, $
|
|
$ γ′(t)+σ22tα−1Γ(α)(T−tT)2=0, $
|
with the terminal condition
|
$ β(T)=γ(T)=δ(T)=0. $
|
By calculating we have
|
$ β(t)=r(T−t), $
|
|
$ δ(t)=r2T(T−t)2−σ22αΓ(α)(Tα−tα)+σ22T(α+1)Γ(α)(Tα+1−tα+1), $
|
|
$ γ(t)=σ22αΓ(α)(Tα−tα)−σ2T(α+1)Γ(α)(Tα+1−tα+1)+σ22T2(α+2)Γ(α)(Tα+2−tα+2). $
|
Then from Eqs (3.13) and (3.15), the cauchy problem Eq (3.12) changes into
|
$ {∂W∂τ−∂2W∂η2=0,W(0,η)=(eη−K)+. $
|
(3.16) |
According to heat equation theory, the solution to Eq (3.16) is given by
|
$ W(τ,η)=12√πτ∫+∞−∞(ey−K)+e−(y−η)24τdy, $
|
(3.17) |
By utilizing the inverse transformation of variables and algebraic operation to Eq (3.17), we can obtain the pricing formula of a fixed strike geometric average Asian call option Eq (3.9).
Remark 3.1. It is not to obtain that $ \gamma'(t) < 0 $, thus the maximum value of $ \gamma(t) $ is $ \gamma(0) = \frac{\sigma^2 T^{\alpha}}{\alpha (\alpha+1)(\alpha+2)\Gamma(\alpha)} $.
Remark 3.2. We can obtain the pricing formula for a floating strike geometric average Asian call option by using Fourier transform. Please refer to the Appendix for further details.
Furthermore, we can obtain the following Theorem.
Theorem 3.3. The put-call parity relationship for the fixed strike geometric average Asian option can be given by
|
$ V(t,S,J)−P(t,S,J)=a(t)JtTST−tT−Ke−r(T−t). $
|
(3.18) |
where $ P(t, S, J) $ is the price of the fixed strike geometric average Asian put option and
|
$ a(t)=eσ22(α+1)Γ(α)T(tα+1−Tα+1)+σ22(α+2)Γ(α)T2(Tα+2−tα+2)+r2T(t2−T2). $
|
Proof of Theorem 3.3
Letting
|
$ H(t,S,J)=V(t,S,J)−P(t,S,J). $
|
(3.19) |
Theorem 3.1 leads that $ H(t, S, J) $ satisfies the following PDE
|
$ ∂H∂t+12σ2tα−1Γ(α)S2∂2H∂S2+JlnS−lnJt∂H∂J+rS∂H∂S−rH=0, $
|
(3.20) |
with the terminal condition
|
$ H(T,S,J)=J−K. $
|
(3.21) |
Take the transformation Eq (3.10), we can obtain
|
$ ∂H∂t+12σ2tα−1Γ(α)(T−tT)2∂2H∂ξ2+[r−12σ2tα−1Γ(α)]T−tT∂H∂ξ−rH=0, $
|
(3.22) |
and
|
$ H(T)=eξ−K. $
|
(3.23) |
Denote
|
$ H=a(t)eξ+b(t). $
|
(3.24) |
Substituting Eq (3.24) into Eq (3.22) we can obtain
|
$ {a′(t)+12σ2tα−1Γ(α)(T−tT)2a(t)+[r−12σ2tα−1Γ(α)]T−tTa(t)−ra(t)=0,a(T)=1. $
|
(3.25) |
and
|
$ {b′(t)−rb(t)=0,b(T)=−K. $
|
(3.26) |
Solving Eq (3.25) and Eq (3.26), we have
|
$ a(t)=eσ22(α+1)Γ(α)T(tα+1−Tα+1)+σ22(α+2)Γ(α)T2(Tα+2−tα+2)+r2T(t2−T2), $
|
(3.27) |
|
$ b(t)=−Ke−r(T−t). $
|
(3.28) |
Substituting Eqs (3.27) and (3.28) into Eq (3.24), we can derive
|
$ V(t,S,J)−P(t,S,J)=a(t)JtTST−tT+b(t). $
|
(3.29) |
Proof is completed.
In this section, we will give some numerical results. Theorem 3.2 leads the following results.
Corollary 4.1. When $ t = 0 $, the price of a fixed strike geometric average Asian call option $ \hat{V}(K, T) $ is given by
|
$ ˆV(K,T)=S0eδ(0)+σ22(ˆa∗+ˆb∗)−rTΦ(^d1)−Ke−rTΦ(^d2), $
|
(4.1) |
where
|
$ δ(0)=rT2−σ22αΓ(α)Tα+σ2Tα2(α+1)Γ(α), $
|
|
$ ^d1=ln(S0K)+δ(0)+σ2(ˆa∗+ˆb∗)σ√ˆa∗+ˆb∗, $
|
|
$ ^d2=^d1−σ√ˆa∗+ˆb∗, $
|
|
$ ˆa∗=TααΓ(α)−2Tα(α+1)Γ(α), $
|
and
|
$ ˆb∗=Tα(α+2)Γ(α). $
|
Corollary 4.2. Letting $ \alpha \uparrow 1 $, then from Theorem 3.2 we can obtain the price of a fixed strike geometric average Asian call option $ V(t, S, J) $ is given by
|
$ V(t,S,J)=(JtS(T−t))1Te˜δ(t)+σ22(˜a∗+˜b∗)−r(T−t)Φ(~d1)−Ke−r(T−t)Φ(~d2), $
|
(4.2) |
|
$ ˜δ(t)=r2T(T−t)2−σ22(T−t)+σ24T(T2−t2), $
|
|
$ ~d1=ln(Jt/TS(T−t)/TK)+˜δ(t)+σ2(˜a∗+˜b∗)σ√˜a∗+˜b∗, $
|
|
$ ~d2=~d1−σ√˜a∗+˜b∗, $
|
|
$ ˜a∗=t2−TtT, $
|
|
$ ˜b∗=T3−t33T2, $
|
this is consistent with the result in [10,12].
par From figure 1, we can see that the value of $ V_{\alpha}(K, T) $ decreases with $ K $ increases and increases with $ T $ increases.
From Figure 2, we can see that the price of a fixed strike geometric average Asian call option in subdiffusive regime ($ V_{\alpha}(K, T) $) is decrease with the increase of $ \alpha $. Furthermore, when $ \alpha\uparrow 1 $, reduces to the "objective time" $ t $, then the price of a fixed strike geometric average Asian call option in subdiffusive regime is larger than the price of a fixed strike geometric average Asian call option in Brownian motion regime.
From Figure 3, it is obviously to see that the price of a fixed strike geometric average Asian call option in subdiffusive regime ($ V_{\alpha}(K, T) $) is usually larger than that in Brownian motion regime $ V_{B}(K, T) $. Specially, the value of $ V_{\alpha}(K, T)-V_{B}(K, T) $ decrease as $ K $ increases.
The Asian options have been traded in major capital markets, and offer great flexibility to the market participants. Therefore, it is important to price them accurately and efficiently both in theory and practice. In order to capture the periods of constant values property in the dynamics of underlying asset price, this paper discuss the pricing problem of the fixed strike geometric Asian option under a subdiffusive regime. We derive both subdiffusive partial differential equations and explicit formula for geometric Asian option by using delta-hedging strategy and partial differential equation method. Furthermore, numerical studies are performed to illustrate the performance of our proposed pricing model.
This work was supported by the Natural Science Foundation of Anhui province (No.1908085QA29) and the Natural Science Foundation of Jiangxi Educational Committee (No. GJJ170472).
The authors declared that they have no conflicts of interest to this work.
| [1] | Bodenheimer T, Wagner EH, Grumbach K. Improving primary care for patients with chronic illness JAMA 2002; 288: 1775-1779. |
| [2] | Bodenheimer T, Wagner EH, Grumbach K. Improving primary care for patients with chronic illness: the chronic care model, Part 2 JAMA 2002; 288:1909-1914. |
| [3] | Wagner EH, Austin BT, Von Korff M. Organizing care for patients with chronic illness Milbank Q 1996; 74: 511-544. |
| [4] | Wagner EH. Chronic disease management: What will it take to improve care for chronic illness? Eff Clin Pract 1998: 2-4. |
| [5] | Darves B. Patient registries: A key step to quality improvement. 2005http://phstwlp1.partners.org:2387/clinical_information/journals_publications/acp_internist/sep05/patient.htm 2004. Accessed Jan 25, 2010. |
| [6] | Schmittdiel J, Bodenheimer T, Solomon NA, Gillies RR, Shortell SM. Brief report: The prevalence and use of chronic disease registries in physician organizations. A national survey. J Gen Intern Med 2005; 20: 855-858. |
| [7] | Jamtvedt G, Young JM, Kristoffersen DT, Thomson O'Brien MA, Oxman AD. Audit and feedback: Effects on professional practice and health care outcomes Cochrane Database Syst Rev 2003. CD000259. |
| [8] | Weingarten SR, Henning JM, Badamgarav E, et al. Interventions used in disease management programmes for patients with chronic illness-which ones work?. Meta-analysis of published reports. BMJ 2002; 325: 925. |
| [9] | Kenealy T, Arroll B, Petrie KJ. Patients and computers as reminders to screen for diabetes in family practice. Randomized-controlled trial. J Gen Intern Med 2005; 20: 916-921. |
| [10] | Stroebel RJ, Scheitel SM, Fitz JS, et al. A randomized trial of three diabetes registry implementation strategies in a community internal medicine practice Jt Comm J Qual Improv 2002; 28: 441-450. |
| [11] | Grant RW, Hamrick HE, Sullivan CM, et al. Impact of population management with direct physician feedback on care of patients with type 2 diabetes Diabetes Care 2003; 26: 2275-2280. |
| [12] | Harris MF, Priddin D, Ruscoe W, Infante FA, O'Toole BI. Quality of care provided by general |
| [13] | practitioners using or not using division-based diabetes registers Med J Aust 2002; 177: 250-252. |
| [14] | 13. Karter AJ, Parker MM, Moffet HH, et al. Missed appointments and poor glycemic control: An opportunity to identify high-risk diabetic patients Med Care 2004; 42: 110-115. |
| [15] | 14. Renders CM, Valk GD, Griffin S, Wagner EH, Eijk JT, Assendelft WJ. Interventions to improve the management of diabetes mellitus in primary care, outpatient and community settings Cochrane Database Syst Rev 2001. CD001481. |
| [16] | 15. Use of patient registries in US. primary care practices Am Fam Physician 2007; 75: 9. |
| [17] | 16. Davis DA, Thomson MA, Oxman AD, Haynes RB. Changing physician performance. A systematic review of the effect of continuing medical education strategies. JAMA 1995; 274: 700-705. |
| [18] | 17. Lorig KR, Ritter P, Stewart AL, et al. Chronic disease self-management program: 2-year health status and health care utilization outcomes Med Care 2001; 39: 1217-1223. |
| [19] | 18. Ferguson JA, Weinberger M. Case management programs in primary care J Gen Intern Med 8; 13: 123-126. |
| [20] | 19. Rich MW, Beckham V, Wittenberg C, Leven CL, Freedland KE, Carney RM. A multidisciplinary intervention to prevent the readmission of elderly patients with congestive heart failure N Engl J Med 1995; 333: 1190-1195. |
| [21] | 20. Al Rubeaan K A, Youssef A M Subhani SN, Ahmad NA, Al Sharqawi AH and Ibrahim HM.A Web-Based Interactive Diabetes Registry for Health Care Management and Planning in Saudi Arabia. J Med Internet Res. 2013;15(9): e202.. doi: 10.6/jmir.2722 |
| [22] | 21. Geraghty EM, Balsbaugh T, Nuovo, J, and Sanjeev Tandon S. Using Geographic Information Systems (GIS) to Assess Outcome Disparities in Patients with Type 2 Diabetes and Hyperlipidemia. JABFM. 2010;23(1);88 - 96. doi: 10.31jabfm.2010.01.090149 |
| [23] | 22. Curtis A Kothari C, Paul R and Connors E. Using GIS and Secondary Data to Target Diabetes-Related Public Health Efforts . Public Health Reports. 2013; 128: 212-220. |
| [24] | 23. Ministry of Health. Eastern Regional Health Authority,Trinidad and Tobago. |
| [25] | http://www.health.gov.tt/sitepages/default.aspx?id=90. Accessed Jan 26, 2010. |
| [26] | 24. The CDEMS User Network.CDEMS Basics.Washington.2010. |
| [27] | http://www.cdems.com/. Accessed Jan 26, 2010 |
| [28] | 25. Diabetes Guidelines.A Desktop Guide to Type 2 Diabetes. Brussels: International Diabetes Federation. http://www.staff.ncl.ac.uk/philip.home/t2dg1999. Accessed Feb9, 2010 |
| [29] | 26. Diagnosis and Classification of Diabetes Mellitus. Diabetes Care 1997; 20: 1183-97. http://www.staff.ncl.ac.uk/philip.home/who_dmc.htm Accessed Feb 9, 2010. |
| [30] | 27. The WHO classification for obesity http://apps.who.int/bmi/index.jsp?introPage=intro_3.html |
| [31] | 28. James PA, Oparil S, Carter BL, et al. 2014 Evidence-Based Guideline for the Management of High Blood Pressure in Adults: Report From the Panel Members Appointed to the Eighth Joint National Committee (JNC 8). JAMA. 2014; (5): 507-520. |
| [32] | 29. WHO Laboratory Diagnosis and monitoring of Diabetes Mellitus Manual, 2002. WHO Geneva. |
| [33] | 30. Pinhas-Hamiel O, Zeitler P. The global spread of type 2 diabetes mellitus in children and adolescents. J Pediatr 2005; 146: 693-700. |
| [34] | 31. MODY - It's Not Type 1 and Not Type 2, but Something Else. http://www.phlaunt.com/diabetes/14047009.php Accessed July 14, 2010. |
| [35] | 32. Defronzo RA. Banting Lecture. From the triumvirate to the ominous octet: a new paradigm for the treatment of type 2 diabetes mellitus. Diabetes 2009; 58: 773-795. |
| [36] | 33. Fagot-Campagna A, Pettitt DJ, Engelgau MM, Burrows NR, Geiss LS, Valdez R, Beckles GL, Saaddine J, Gregg EW, Williamson DF, Narayan KM.Type 2 diabetes among North American children and adolescents: an epidemiologic review and a public health perspective.J Pediatr. 2000 May; 15): 664-72. |
| [37] | 34. Poon King T, Henry MV, Rampersad F. Prevalence and natural history of diabetes in Trinidad. The Lancet. January 27 1968; 155-160. |
| [38] | 35. GJ Miller, GH Maude, GL Beckles: Incidence of HTN and Non- Insulin Dependent Diabetes Mellitus and associated risk factors in a rapidly developing Caribbean community: The St. James survey, Trinidad. Journal of Epidemiology and Community Health 1996; 50: 497-504. http://www.jstor.org/pss/25568320. |
| [39] | 36. Chadee D, Seemungal T, Pinto Pereia LM, Chadee M, Maharaj R and Teelucksingh S. Prevalence of self-reported diabetes, hypertension and heart disease in individuals seeking state funding in Trinidad and Tobago, West Indies. J Epid Glo Hea. 2013; 3(2): 95-103. |
| [40] | 37. American Diabetes Association. Microvascular complications and foot care. Sec. 9. In Standards of Medical Care in Diabetes—2015. Diabetes Care 2015; 38(Suppl. 1):S58-S66. |
| [41] | 38. Boda P. Availability and accessibility of diabetes clinics on Trinidad: An analysis using proximity tools in a GIS environment. Health. 2013; 5(11B): 35-42. |
| [42] | 39. Diabetes care and research in Europe: the Saint Vincent Declaration. Diabet Med 1990;7: 360. |
| [43] | 40. Mungrue K. Are segments of the developing world competing in end-stage renal disease (ERSD)? NDT Plus (2008) 1 (4): 240 doi: 10.1093/ndtplus/stn067. |
| [44] | 41. The WHO classification for obesity. http://apps.who.int/bmi/index.jsp?introPage=intro_3.html |
| [45] | 42. Philip A. Ades, MD and Patrick D.Savage, MS. The Obesity Paradox: Perception vs Knowledge doi: 10.4065/mcp.2009.0777 Mayo Clinic Proceedings February 2010 vol. 85 no. 2 112-114). |
| [46] | 43. Ford ES, Ajani UA, Croft JB, Critchley JA, Labarthe DR, Kottke TE, et al. Explaining the decrease in U.S. deaths from coronary disease, 1980-2000. N Engl J Med 2007; 356: 2388-98. |
| [47] | 44. Gregg EW, Cadwell BL, Cheng YJ, Cowie CC, Williams DE, Geiss L et al. Trends in the prevalence and ratio of diagnosed to undiagnosed diabetes according to obesity levels in the US Diabetes Care2004; 27: 2806-12. |
| [48] | 45. 2013 ACC/AHA Guideline on the Treatment of Blood Cholesterol to Reduce Atherosclerotic Cardiovascular Risk in Adults: A Report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines. Neil J. Stone, et al. Circulation. 2014;129:S1-S45. |
| [49] | 46. Mokdad AH, Ford ES, Bowman BA, Dietz WH, Vinicor F, Bales VS, et al. Prevalence of obesity, diabetes, and obesity-related health risk factors, 2001. JAMA2003; 289: 76-9. |
| [50] | 47. Konzem S, Pharm.D. Controlling Hypertension in Patients with Diabetes, Am Fam Physician. 2002 Oct 1; 66(7): 1209-1215. |
| [51] | 48. Sowers JR, Epstein M and Frohlich E D. Diabetes, Hypertension, and Cardiovascular Disease : An Update Hypertension 2001; 37; 1053-1059. |
| [52] | 49. Ricardo Padilla, Philip S. Mehler. Journal of Women's Health & Gender-Based Medicine. November 2001, 10(9): 897-905. doi:10.1089/160901753285804. |
| [53] | 50. Bodenheimer T, Wang MC, Rundall TG, et al. What are the facilitators and barriers in physician organizations' use of care management processes? Jt Comm J Qual Saf 2004; 30505-4. |
| 1. | Maria A. Augustyniak-Jabłokow, Raanan Carmieli, Roman Strzelczyk, Ryhor Fedaruk, Krzysztof Tadyszak, Electron Spin Echo Studies of Hydrothermally Reduced Graphene Oxide, 2021, 125, 1932-7447, 4102, 10.1021/acs.jpcc.0c11316 | |
| 2. | Maocong Hu, Zhenhua Yao, Xianqin Wang, Characterization techniques for graphene-based materials in catalysis, 2017, 4, 2372-0484, 755, 10.3934/matersci.2017.3.755 | |
| 3. | Maria A. Augustyniak-Jabłokow, Krzysztof Tadyszak, Roman Strzelczyk, Ryhor Fedaruk, Raanan Carmieli, Slow spin relaxation of paramagnetic centers in graphene oxide, 2019, 152, 00086223, 98, 10.1016/j.carbon.2019.06.024 | |
| 4. | Maria A. Augustyniak-Jabłokow, Ryhor Fedaruk, Roman Strzelczyk, Łukasz Majchrzycki, Identification of a Slowly Relaxing Paramagnetic Center in Graphene Oxide, 2019, 50, 0937-9347, 761, 10.1007/s00723-018-1058-2 | |
| 5. | Maria A. Augustyniak-Jabłokow, Roman Strzelczyk, Ryhor Fedaruk, Localization of conduction electrons in hydrothermally reduced graphene oxide: electron paramagnetic resonance studies, 2020, 168, 00086223, 665, 10.1016/j.carbon.2020.07.023 | |
| 6. | Francesco Tampieri, Antonio Barbon, Matteo Tommasini, Analysis of the Jahn-Teller effect in coronene and corannulene ions and its effect in EPR spectroscopy, 2021, 2, 26670224, 100012, 10.1016/j.chphi.2021.100012 | |
| 7. | Damian Tomaszewski, Krzysztof Tadyszak, Electron Spin Relaxation in Carbon Materials, 2022, 15, 1996-1944, 4964, 10.3390/ma15144964 | |
| 8. | Asya Svirinovsky-Arbeli, Raanan Carmieli, Michal Leskes, Multiple Dynamic Nuclear Polarization Mechanisms in Carbonaceous Materials: From Exogenous to Endogenous 13C Dynamic Nuclear Polarization-Nuclear Magnetic Resonance up to Room Temperature, 2022, 126, 1932-7447, 12563, 10.1021/acs.jpcc.2c02470 | |
| 9. | Nuralmeera Balqis, Badrul Mohamed Jan, Hendrik Simon Cornelis Metselaar, Akhmal Sidek, George Kenanakis, Rabia Ikram, An Overview of Recycling Wastes into Graphene Derivatives Using Microwave Synthesis; Trends and Prospects, 2023, 16, 1996-1944, 3726, 10.3390/ma16103726 | |
| 10. | Antonio Barbon, 2018, 978-1-78801-372-7, 38, 10.1039/9781788013888-00038 |
Figures(4) / Tables(6)
Mungrue Kameel, Sankar Steven, Kamalodeen Aleem, Lalchansingh Dayna, Ramnarace Demeytri, Samodee Shanala, Sookhan Craig, Sookar Navin, Sooknanan Kristal, St.George Leah, Suruj Deonath. Evaluation and Use of Registry Data in a GIS Analysis of Diabetes[J]. AIMS Public Health, 2015, 2(3): 318-331. doi: 10.3934/publichealth.2015.3.318
DownLoad:
