We consider an optimal investment model in which the goal is to maximize long‐term growth rate of expected utility wealth. In model, mean returns securities are explicitly affected by underlying economic factors. The function HARA. problem reformulated as infinite time horizon risk‐sensitive control problem. study dynamic programming equation associated with this and derive some consequences

Abstract A RP‐HPLC method for determining fourteen components (gallic acid, chebulic 1,6‐di‐ O ‐galloyl‐D‐glucose, punicalagin, 3,4,6‐tri‐ casuarinin, chebulanin, corilagin, neochebulinic terchebulin, ellagic chebulagic chebulinic and 1,2,3,4,6‐penta‐ ‐galloyl‐D‐glucose) in the fruit of Terminalia chebula Retz. is described. The separation was achieved within 80 min using a binary gradient with mobile phases consisting pH 2.7 phosphoric acid solution an 80% CH 3 CN solution. Capillary...

We consider an optimal investment problem proposed by Bielecki and Pliska. The goal of the is to optimize long-term growth expected utility wealth. HARA functions with exponent $-\infty< \gamma< 1$. can be reformulated as infinite time horizon risk-sensitive control problem. Some useful ideas results from theory used in analysis. Especially, we analyze associated dynamical programming equation. Then (or approximately optimal) Markovian policy derived.

Let $\pi(x)$ be a given probability density proportional to $\exp(-U(x))$ in high-dimensional Euclidean space $\mathbb{R}^m$. The diffusion $dX(t) = -\nabla U(X(t))dt + \sqrt 2 dW(t)$ is often used sample from $\pi$. Instead of $-\nabla U(x)$, we consider diffusions with smooth drift $b(x)$ and having equilibrium $\pi(x)$. First study some general properties then concentrate on the Gaussian case, namely, U(x) Dx$ strictly negative-definite real matrix $D$ $b(x) Bx$ stability $B$; that is,...

Let U be a given function defined on ℝd and π(x) density proportional to exp−U(x). The following diffusion X(t) is often used sample from π(x), $$dX(t)=-\nabla U(X(t))\,dt+\sqrt{2}\,dW(t),\qquad X(0)=x_{0}.$$ To accelerate the convergence, family of diffusions with as their common equilibrium considered, $$dX(t)=\bigl(-\nabla U(X(t))+C(X(t))\bigr)\,dt+\sqrt{2}\,dW(t),\qquad LC corresponding infinitesimal generator. spectral gap in L2(π) (λ(C)), convergence exponent π variational norm (ρ(C)),...

In this paper we study the transition density $P_t(x, y)$ of a nondegenerate diffusion process by using stochastic control method invented Fleming and idea parallel translation. We obtain two-sided estimate for as well some bounds derivatives $\log P_t(x, y)$.

An optimal investment policy model for the long term growth of expected utility wealth is considered. The function HARA with exponent $-\infty < \gamma 1$. problem can be reformulated as an infinite time horizon, risk sensitive control problem. Then dynamic programming equations different exponents and constraints are studied. We obtain some estimates solution each equation. This used to derive interesting properties.

A total of 37 commercial samples Ginseng Radix, the origins which belonged to Panax ginseng C. A. Meyer, P. quinquefolia Linn. (American ginseng), and notoginseng Burkill (sanchi-ginseng), respectively, were collected from Taiwan herbal markets. The contents nine ginsenosides, Rb(1), Rb(2), Rc, Rd, Re, Rf, Rg(1), Rg(2), R(0), three malonylginsenosides, mRb(1), mRb(2), mRc, in these determined by high-performance liquid chromatography. It was found that saponin generally higher than ginseng....

SUMMARY Sampling from a Markov random field II can be performed efficiently via Monta Carlo methods by simulating chain that converges weakly to II. We consider class of local updating dynamics are reversible with respect It includes the Metropolis algorithm (MA) and Gibbs sampler (GS). investigate speed weak convergence these chains in terms their second-largest eigenvalues absolute value. study general algebraic structure then stochastic Ising model detail. conclude following: GS is faster...

Bellman equations of ergodic type related to risk-sensitive control are considered. We treat the case that nonlinear term is positive quadratic form on first-order partial derivatives solution, which includes linear exponential Gaussian problem. In this paper we prove equation in general has multiple solutions. shall specify set all classical solutions and classify by a global behavior diffusion process associated with given solution. The solution plays particular role. also uniqueness such...

We study the large time behavior of solutions to Cauchy problem for semilinear parabolic equations having quadratic nonlinearity in gradients. Equations this kind appear stochastic control theory. It turns out that as tends infinity solution converges a associated ergodic problem. Our approach relies on PDE and probabilistic arguments.

A total of 22 commercial Ephedra herba samples which belonged to EPHEDRA SINICA, E. INTERMEDIA, EQUISETINA, and DISTACHYA, respectively, were collected from the Taiwan herbal market. The contents six ephedrine alkaloids - (E), pseudoephedrine (PE), methylephedrine (ME), methyl-pseudoephedrine (MPE), norephedrine (NE), nor-pseudoephedrine (NPE) in these determined by capillary electrophoresis found differ greatly among samples. Generally, SINICA was superior (1.594 +/- 0.467%) INTERMEDIA...

Rhubarb (Rhei rhizoma), a commonly used Chinese herb, contains anthraquinones, anthrones, galloylglucoses, stilbenes, and flavan-3-ols compounds, etc. as major constituents. Using 19 of these compounds markers, an HPLC-UV-MS method was developed to estimate the quality rhubarb samples within period 70 min. Extracts were analyzed with Cosmosil 5C18-MS column eluted gradient comprising aqueous solution acetic acid methanol at flow rate 0.9 mL/min. Peaks detected by absorbance measurements 254...

We analyze the behavior of spectral gap Laplace- Beltrami operator on a compact Riemannian manifold when divergence-free drift vector field is added. increase by multiplication with large constant <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="c"> <mml:semantics> <mml:mi>c</mml:mi> <mml:annotation encoding="application/x-tex">c</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and ask question how behaves as goes to...

We consider a long-term optimal investment problem where an investor tries to minimize the probability of falling below target growth rate. From mathematical viewpoint, this is large deviation control problem. This will be shown relate risk-sensitive stochastic for sufficiently time horizon. Indeed, in our theorem we state duality relation between above two problems. Furthermore, under multidimensional linear Gaussian model obtain explicit solutions primal

Abstract Angelicae Radix (AR) and Ligustici Rhizoma (LR) are both derived from the Umbelliferae plants contain similar organic acids as their bioactive compounds. Nine of these acids, including nicotinic acid, protocatechuic phthalic folinic p ‐hydroxybenzoic folic vanillic caffeic ferulic acid were separated by HPLC CE. Detection at 210 nm with a linear gradient containing 20 mM KH 2 PO 4 (pH 3.5) H O–CH 3 CN in buffer solution 10 LTAC, Na HPO , 9 B O 7 9.56), CH CE found to be most...