Report : review of the literature : maintenance and rehabilitation costs for roads (Risk-based Analysis)

Realistic estimates of short- and long-term (strategic) budgets for maintenance and rehabilitation of road assessment management should consider the stochastic characteristics of asset conditions of the road networks so that the overall variability of road asset data conditions is taken into account. The probability theory has been used for assessing life-cycle costs for bridge infrastructures by Kong and Frangopol (2003), Zayed et.al. (2002), Kong and Frangopol (2003), Liu and Frangopol (2004), Noortwijk and Frangopol (2004), Novick (1993). Salem 2003 cited the importance of the collection and analysis of existing data on total costs for all life-cycle phases of existing infrastructure, including bridges, road etc., and the use of realistic methods for calculating the probable useful life of these infrastructures (Salem et. al. 2003). Zayed et. al. (2002) reported conflicting results in life-cycle cost analysis using deterministic and stochastic methods. Frangopol et. al. 2001 suggested that additional research was required to develop better life-cycle models and tools to quantify risks, and benefits associated with infrastructures. It is evident from the review of the literature that there is very limited information on the methodology that uses the stochastic characteristics of asset condition data for assessing budgets/costs for road maintenance and rehabilitation (Abaza 2002, Salem et. al. 2003, Zhao, et. al. 2004). Due to this limited information in the research literature, this report will describe and summarise the methodologies presented by each publication and also suggest a methodology for the current research project funded under the Cooperative Research Centre for Construction Innovation CRC CI project no 2003-029-C

Homogeneous discrete time alternating compound renewal process: A disability insurance application

Discrete time alternating renewal process is a very simple tool that permits solving many real life problems. This paper, after the presentation of this tool, introduces the compound environment in the alternating process giving a systematization to this important tool.The claim costs for a temporary disability insurance contract are presented. The algorithm and an example of application are also provide

High frequency trading and asymptotics for small risk aversion in a Markov renewal model

We study a an optimal high frequency trading problem within a market microstructure model designed to be a good compromise between accuracy and tractability. The stock price is driven by a Markov Renewal Process (MRP), while market orders arrive in the limit order book via a point process correlated with the stock price itself. In this framework, we can reproduce the adverse selection risk, appearing in two different forms: the usual one due to big market orders impacting the stock price and penalizing the agent, and the weak one due to small market orders and reducing the probability of a profitable execution. We solve the market making problem by stochastic control techniques in this semi-Markov model. In the no risk-aversion case, we provide explicit formula for the optimal controls and characterize the value function as a simple linear PDE. In the general case, we derive the optimal controls and the value function in terms of the previous result, and illustrate how the risk aversion influences the trader strategy and her expected gain. Finally, by using a perturbation method, approximate optimal controls for small risk aversions are explicitly computed in terms of two simple PDE's, reducing drastically the computational cost and enlightening the financial interpretation of the results.Comment: 30 pages, new asymptotic results, typos corrected, new bibliographical reference