Stochastic Model

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Stochastic Model to Find the Effect of Glucose-Dependent Insulinotropic Hormone in Cholecystectomized Patients Using Boundary Condition in Hamilton Jacobi-Bellmann Equation Dr. P. Senthil Kumar* & R. Abirami** * Assistant Professor, Department of Mathematics, Rajah Serfoji Government Arts College, Thanjavur, Tamilnadu, India. Email: senthilscas@yahoo.com ** Assistant Professor, Department of Basic Science and Humanities, Ponnaiyah Ramajayam Engineering College, Thanjavur, Tamilnadu, India. Email: abijai100@gmail.com Abstract: The purpose of the Study was to evaluate the effect gut hormones with focus on Glucose-dependent Insulinotropic Hormone (GIP) in ten cholecystectomized subjects and ten healthy humans.…show more content…
Notations: B Brownian motion Y State process σ Stochastic process Z Value function δ Relative risk aversion coefficient 3. Stochastic Model: Let be a complete probability space on which we define a two-dimensional standard Brownian motion and we also fix a time interval . Let be the augmentation of the filtration , . Let Y be an Ornstein-Uhlenbeck process: (1) We call Y a state process, because it determines an investment opportunity set in our portfolio problem. There is one riskless asset and one risky asset. Suppose the price of the riskless asset satisfies Where is constant. The risky asset price A satisfies the stochastic differential equation (2) Where satisfies Then (2) can be written…show more content…
Example: Ten cholecystectomized subjects and 10 healthy control subjects were included in the study. The subjects were without diabetes and had normal glucose tolerance according to 75-g oral glucose tolerance test. The plasma concentration of GIP was measured by radioimmunoassay. The subjects were given a standardized fat-rich liquid meal (2,200kJ). The plasma concentration of total GIP is shown in figure (1). The basal plasma concentrations were observed in the two groups. It was found that there was no difference in basal values or postprandial responses in cholecystectomized subjects compared with control subjects. Cholecystectomy did not have a major impact on gastro intestinal hormones [2]. Figure: (1) Figure: (2) 5. Conclusion: Evaluations of the effect gut hormones with focus on Glucose-dependent Insulinotropic Hormone (GIP) in ten cholecystectomized subjects and ten healthy humans. The concentration of GIP was similar in the two groups. In this paper, the problem is investigated by considering the boundary condition of Hamilton Jacobi-Bellmann equation. The result coincides with the mathematical and medical

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