Qiying Hu

Performance analysis of sequential Internet auction systems comparing with fixed price case

In this paper, we first present a new performance model and an analysis for its optimal allocation in a sequential Internet auction system with a fixed reserve price. In such a system, a seller wants to sell a given amount of items through sequential auctions on the Internet. The seller has a reserve price for each item. For each auction, the seller should allocate a quantity of items from the total available items to be auctioned. The buyers arrive according to a Poisson process and bid honestly (without collusion, etc.). We consider the sequential Internet auction model to be a Markov decision process and present its performance analysis for the Internet auction model. In the analysis, we show that the result is no difference whether the reserve price is private (known only to the seller) or public (posted on the web). Then we show that in the monotonous properties of the optimal policy, the more items are in hand or the less the horizons remain, the more items are allocated for auction. Next, we compare this auction mechanism with mechanisms of fixed price, dynamic price and sequential auction with dynamic reserve price, respectively, for the sellers profit and show that the seller will receive more in the auction case than in the price case and more in the dynamic case than in the fixed price case, respectively. Finally, numerical results are given, where we compute the maximal expected total revenue and the solution of the optimal allocation, display the effect of the arrival rate, and discuss the optimal reserve price and the available number of auctions.

A Method on Solving Multiobjective Conditional Value-at-Risk

This paper studies Conditional Value-at-Risk (CVaR) with multiple losses. We introduce the concept of α-CVaR for the case of multiple losses under the confidence level vector α. The α-CVaR indicates the conditional expected losses corresponding to the α-VaR. The problem of solving the minimal α-CVaR results in a multiobjective problem (MCVaR). In order to get Pareto efficient solutions of the (MCVaR), we introduce a single objective problem (SCVaR) and show that the optimal solutions of the (SCVaR) are the Pareto efficient solutions of (MCVaR).

Continuous time Markov decision processes with expected discounted total rewards

This paper discusses continuous time Markov decision processes with criterion of expected discounted total rewards, where the state space is countable, the reward rate function is extended real-valued and the discount rate is a real number. Under necessary conditions that the model is well defined, the state space is partitioned into three subsets, on which the optimal value function is positive infinity, negative infinity, or finite, respectively. Correspondingly, the model is reduced into three submodels, by generalizing policies and eliminating some worst actions. Then for the submodel with finite optimal value, the validity of the optimality equation is shown and some its properties are obtained.

Analysis for some properties of discrete time Markov decision processes

This paper investigates properties of the optimality equation and optimal policies in discrete time Markov decision processes with expected discounted total rewards under weak conditions that the model is well defined and the optimality equation is true. The optimal value function is characterized as a solution of the optimality equation and the structure of optimal policies is also given.

A unified model for state feedback of discrete event systems II: Control synthesis problems

This paper studies control synthesis problems in a new model framework for discrete event state feedback control systems. The new model framework consists of a basis model as well as concurrent models. We study relationships between the basis model and the concurrent models from the perspective of a predicate being controllable and synthesizable. We derive a linear order for the models, and moreover, show that they are equivalent under certain conditions. Based on this, three conditions are presented for synthesizing a predicate completely. Finally, the optimal control synthesis problem for both the basis model and the concurrent models is studied.

Market-based interest rates: deterministic volatility case

Central banks issue often many kinds of bonds to guide their benchmark interest rates. Their market data are thought of to reflect current state of the countries financial system. Then at least how much data is needed? Based on the framework of HJM model, We prove that the amount of the data needed is related to the form of the volatility function of forward rates, and then the initial forward rate curve is not essential.