“Notoriously, works on mathematical finance can be precise, and they can be comprehensible. Sadly, as Dr. Johnson might have put it, the ones which are precise are not necessarily comprehensible, and those comprehensible are not necessarily precise.” So starts the preface to Baxter and Rennie's recent treatise on financial calculus. The book attempts to give an introduction to modern continuous time finance in a precise and comprehensible fashion. Does it succeed? Yes, it is a very clear and precise little (233 pages) book, although the claim that the book is accessible to a reader with only “some knowledge of (classical) differential calculus and experience with symbolic notation” is exaggerated. Such a reader would find the material hard going indeed.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0266466698143050

FINANCIAL CALCULUS: AN INTRODUCTION TO DERIVATIVE PRICING: Martin Baxter and Andrew Rennie, Cambridge University Press, 1996

A method for determining optimal risk-based maintenance and rehabilitation (M&R) policies for transportation infrastructure is presented. The proposed policies guarantee a certain performance level across the network under a predefined level of risk. The long-term model is formulated in the Markov Decision Process framework with risk-averse actions and transitional probabilities describing the uncertainty in the deterioration process. The well known Conditional Value at Risk (CVaR) is used as the measure of risk. The steady-state risk-averse M&R policies are modeled assuming no budget restriction. To address the short-term resource allocation problem, two linear programming models are presented to generate network-level polices with different objectives. While the proposed methodology is general and can be used with any performance indicator, pavement roughness is used for numerical studies and an analytical expression for computing CVaR is derived.

Risk-based maintenance and rehabilitation decisions for transportation infrastructure networks

The equilibrium selection approach of Matsui and Matsuyama (J. Econ. Theory65(1995), 415–434) which is based on rational players who maximize their discounted future payoff, is analyzed for symmetric two-player games with a potential function. It is shown that the maximizer of the potential function is the unique state that is absorbing and globally accessible for small discount rates.Journal of Economic LiteratureClassification Number: C72.

Perfect Foresight and Equilibrium Selection in Symmetric Potential Games

Valuing the flexibility of investing in security process innovations

We present a methodology for the joint optimization of rehabilitation and reconstruction activities for heterogeneous pavement systems under multiple budget constraints. The proposed bottom-up approach adopts an augmented condition state to account for the history-dependent properties of pavement deterioration, and solves for steady-state policies for an infinite horizon. Genetic algorithms (GAs) are implemented in the system-level optimization based on segment-specific optimization results. The complexity of the proposed algorithm is polynomial in the size of the system and the policy-related parameters. We provide graphical presentations of the optimal solutions for various budget situations. As a case study, a subset of California’s highway system is analyzed. The case study results demonstrate the economic benefit of a combined rehabilitation and reconstruction budget compared to separate budgets.

A joint bottom-up solution methodology for system-level pavement rehabilitation and reconstruction

This paper focuses upon the optimal repair and inspection policies of infrastructure under uncertainty in the facility deterioration process It is supposed that the condition of the facility, which is defined in continuous state, can only be observed by inspection The optimal impulse control problem is formulated to find out the optimal timing for inspection and repairing so as to minimize the expected life-cycle costs, including the repairing cost, user's cost, and inspection cost The state-dependent rules are presented to determine the optimal timing for inspection and repairing based upon the observation of condition state by solving the second-order Fredholm integral equation The paper concludes with numerical examples, for illustration

Optimal Repair and Inspection Rules under Uncertainty

本研究では経済的寿命に不確実性がある社会基盤施設の最適修繕政策を検討するための方法論を提案する. 社会基盤施設の経済的・物理的劣化過程をマルコフ決定過程としてモデル化する. その上で, 施設管理者が施設の経済便益とライフサイクル費用の双方を考慮しながら, 施設の転用タイミングを決定する最適運営政策と施設の劣化状態を回復する最適修繕政策を同時に決定するための最適アセットマネジメントモデルを定式化する. さらに, 提案した最適アセットマネジメントモデルを港湾施設のアセットマネジメント問題に具体的に適用し, モデルの有効性を実証的に検討する.

https://www.jstage.jst.go.jp/article/jscej1984/2004/772/2004_772_169/_pdf

Optimal repair strategies with reference to economic life expectancy

This paper investigates an economic methodology for project evaluation, which explicitly incorporates evaluation costs and the option value of flexibility in decisions The traditional cost-benefit analysis is fundamentally based upon a 'now or never principle', and fails to evaluate the option value derived by reserving decisions to wait for more concrete information In this paper, the real option model is formulated to determine the optimal timing strategy for project evaluation and implementation The optimal solutions of the model can be obtained by solving the integral equation models This paper is concluded by illustrating numerical examples to demonstrate the availability of the methodology

Optimal timing strategy for project evaluation and implementation

Speed reduction markings (SRMs) on road surface consist of transverse marking lines with decreasing spacing in the direction of vehicle movement. SRMs installed on a straight lane adjacent to a transition curve section contribute to deceleration of the vehicle toward the curve. A leading vehicle’s driver on SRM-installed lane may be exposed to accident risks due to shortage of deceleration and rear-end collision of a following vehicle. To avoid such risks, a layout of spacing intervals among the marking lines of SRMs is required to be optimized according to a speed trajectory of the leading vehicle approaching the curve. The aim of our study is to examine the optimal layout pattern by use of numerical simulation of both the vehicle speed trajectory and the rear-end collision. We construct an optimal control model of driving behavior with speed perception, and we combine it with a car-following model. In the case of SRMs before a sharp bend, our numerical examples showed the results as follows: 1) The layout pattern in which a decreasing rate between the spacing intervals is greater in the end section on SRM-installed lane than in the remaining sections may produce a high risk of the rear-end collision, although the leading vehicle safely enters the curve. 2) The pattern in which the decreasing rate is zero in all sections on SRM-installed lane may produce an accident with which the leading driver meets within the curve, although the rear-end collision risk is very few. These results indicate that the layout pattern of SRMs affecting speed choice of the leading driver toward the curve must consider not only the vehicle speed trajectory of the leading vehicle but also the rear-end collision risk of the following vehicle.

Toshimori Otazawa

Papers

Optimal Repair and Inspection Rules under Uncertainty

Optimal repair strategies with reference to economic life expectancy

Optimal timing strategy for project evaluation and implementation

A simulation study on the pattern of speed reduction markings affecting driver's speed choice before curve entry

Residential land use with demographic dynamics of young and old generations