Robust Dynamic Pricing Over Infinite Horizon in The Presence of Model Uncertainty( 2* Journal)

This paper studies a problem of dynamic pricing faced by a retailer with limited inventory, uncertain about the demand rate model, aiming to maximize expected discounted revenue over an infinite time horizon. The retailer doubts his demand model which is generated by historical data and views it as an approximation. Uncertainty in the demand rate model is represented by a notion of generalized relative entropy process, and the robust pricing problem is formulated as a two-player zero-sum stochastic differential game. The pricing policy is obtained through the Hamilton-Jacobi-Isaacs (HJI) equation. The existence and uniqueness of the solution of the HJI equation is shown and a verification theorem is proved to show that the solution of the HJI equation is indeed the value function of the pricing problem. The results are illustrated by an example with exponential nominal demand rate.

On the solvability of Hamilton's equations in Hilbert spaces

We construct a bounded function $H : l_2\times l_2 \to R$ with continuous Frechet derivative such that for any $q_0\in l_2$ the Cauchy problem $\dot p= - {\partial H\over\partial q}$, $\dot q={\partial H\over\partial p}$, $p(0) = 0$, q(0) = q_0$ has no solutions in any neighborhood of zero in R.

Application of Jacobi algorithm for ISI channels

Here, the Jacobi iterative algorithm is applied to combat intersymbol interference (ISI) caused by frequency-selective channels. The performance bound of the equaliser is analysed in order to gain an insight into its asymptotic behaviour. Because of the error propagation problem, the potential of this algorithm is not reached in an uncoded system. However, its extension to a coded system with the application of the turbo-processing principle results in a new turbo equalisation algorithm, which demonstrates comparable performance with reduced complexity compared with some existing filter-based turbo equalisation schemes; and superior performance compared with some frequency domain solutions, such as orthogonal frequency division multiplexing and single-carrier frequency domain equalisation.

Social determinants of older adults' awareness of community support services in Hamilton, Ontario

Community support services (CSSs) have been developed in Canada and other Western nations to enable persons coping with health or social issues to continue to live in the community. This study addresses the extent to which awareness of CSSs is structured by the social determinants of health. In a telephone interview conducted in February-March 2006, 1152 community-dwelling older adults (response rate 12.4%) from Hamilton, Ontario, Canada were made to read a series of four vignettes and were asked whether they were able to identify a CSS they may turn to in that situation. Across the four vignettes, 40% of participants did name a CSS as a possible source of assistance. Logistic regression was used to determine factors related to awareness of CSSs. Respondents most likely to have awareness of CSS include the middle-aged and higher-income groups. Being knowledgeable about where to look for information about CSSs, having social support and being a member of a club or voluntary organisations are also significant predictors of awareness of CSSs. Study results suggest that efforts be made to improve the level of awareness and access to CSSs among older adults by targeting their social networks as well as their health and social care providers. © 2011 Blackwell Publishing Ltd.