Stochastic Model Research Paper

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: [e-mail]
** Assistant Professor, Department of Basic Science and Humanities, Ponnaiyah Ramajayam Engineering College, Thanjavur, Tamilnadu, India. Email: [e-mail]
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.

The continuous-time portfolio optimization problem in Kim and Omberg [12]. The sufficient conditions to verify that a solution derived from the Hamilton-Jacobi-Bellman equation are in fact an optimal solution to the portfolio selection problem. Many studies have been done on continuous-time portfolio optimization problem with the Merton’s seminal work [1], [7] & [9]. In particular, there has been increasing interest in finding an optiomal portfolio strategy when investment opportunities are stochastic, because many empirical works conclude that investment opportunities are time-varying. There are two main approaches in solving continuous-time portfolio optimization problem. One is the stochastic control approach and the other is the martingale approach. In the stochastic control approach, an optimal solution is conjectured by guessing a solution to the HJB equation. It is necessary to verify that the conjectured solution is in fact solution to the original problem. Korn and kraft [8] pointed out, the verification is often skipped since it is mathematically demanding for kim and omberg examined the finiteness of conjectured value function very carefully, but they could not provide verification conditions. The sufficient condition to verify that the conjectured solution is in fact the solution to the original

A Stochastic process is said to be an admissible portfolio strategy on if
(a)
(b) For some function satisfying the linear growth condition , The set of all admissible strategies on is denoted by . The choice of our set of portfolio strategies seems to be restrictive.
Because of incompleteness there is no unique equivalent martingale measure, and we cannot apply the so-called martingale approach directly. It is thus common to apply the dynamic programming approach using Hamilton-Jacobi-Bellman equation. Let Here and in the sequel, we use the notation
Let We then define by .
The function is called a value function. The Hamilton-Jacobi-Bellman equation related to the problem (5) is (6)
With the boundary condition