Risk results from the direct and indirect adverse consequences of outcomes and events that were not accounted for or that we were ill prepared for, and concerns their effects on individuals, firms or the society at large. It can result from many reasons, both internally induced or occurring externally. In the former case, consequences are the result of failures or misjudgements while in the latter, consequences are the results of uncontrollable events or events we cannot prevent. A definition of risk involves as a result four factors: (i) consequences (ii) their probabilities and their distribution (iii) individual preferences and (iv) collective and sharing effects. Risk is at the kernel of financial theory and practice, insurance, operations risk as well as mathematics (such as applied probability, stochastic modelling and processes, statistics and financial econometrics). Further, risk is of importance and applied to operations, networks and dependent enterprises, environment and technology mananagement. In this broad context, risk has been at the core of my research and course development.
As a result, Risk and Risk Management is relevant to a broad number of fields, each providing a different approach to the quantification, the measurement, the valuation and the management of risk which is motivated by psychological needs and the need to deal with problems that result from uncertainty and the adverse consequences they may induce. Financial economics, for example, deals extensively with hedging problems in order to reduce the risk of a particular portfolio through a trade or a series of trades, or contractual agreements reached to share and induce risk minimization by the parties involved. Financial Risk management, in this special context, consists then in using financial instruments (mostly based on the mathematical modeling and quantification of risk) to negate, prevent or deal ex-post with the effects of risk. By a judicious use of options, contracts, swaps, insurance, an investment portfolio etc. risks can be brought to bearable economic costs. To apply the tools needed to deal with these problems however, it is necessary that extensive research be pursued to guarantee their validity and that students and practitioners alike be trained to appreciate and use properly these (mostly quantitative) tools.
Similarly, engineers and industrial managers are concerned with the many facets of risk. They design processes for reliability, safety and robustness. They do so to reduce failure probabilities and apply robust design techniques to reduce processes’ sensitivity to external and uncontrollable events. In other words, they attempt to render process performance oblivious to events that are undesirable and so can become oblivious to their worst consequences. In this sense, risk assessment and measurement, risk mathematics as well as risk valuation and management are particularly pertinent to operational and technological (risk) management. These two research and educational topics are essential facets of Poly’s academic activities to which the M. Topfer Chair will contribute by initiating and sponsoring collaborative research with other faculty members and course development. In particular, these research efforts may contribute to:
As a result, the M. Topfer Chair research and educational agenda spans broadly two areas, all of which are intertwined in the study and the application of technology to risk, financial risk management, computational finance, Operations and risk externalities. Explicitly, these include:
Finance is essentially motivated by and seeks:
These problems require financial instruments that may deal with the uncertainty and the management of the risks they imply in many different ways. These instruments are often inspired and require the development of mathematical tools. Some instruments merely transfer risk from one period to another and in this sense they manage the time phasing of events to reckon with. An important aspect of such instruments is to supply “immediacy”. Other instruments provide a “spatial” diversification" (in other words the distribution of risks across independent investments) and liquidity. By liquidity, we mean the cost to instantly convert an asset into cash at its fair price. This liquidity is affected both by the existence of a market (in other words, buyers and sellers) as well as the cost of transactions associated to the conversion of the asset into cash. For these reasons, finance gives rise to problems of risk measurement, valuation and computational management requiring both theoretical and applied research.
Research and Applied research in computational finance are numerous and have been applied to motivate students and research by its many opportunities. They include for example, options valuation and management, portfolio analysis and design, credit risks and scoring, market making etc. Options for example, are broadly used for risk management and for speculating, singly or in a combined manner to create desired risk profiles. Beyond theory, practice requires as well that financial engineers be trained in computational finance in order to deal with the construction of portfolios with risk profiles desired by individual investors. This requires an extensive use of mathematical techniques, software and other tools. The number of research projects that have been initiated by supervising research students are as a result extensive and include for example:
The number of applied projects along these lines is particularly important due to Bank’s and financial institutions concerns arising from the Basel 2 new directives.
Insurance is used to substitute payments now for potential damages (reimbursed) later. The size of such payments and the potential damages that may occur with various probabilities lead to widely distributed market preferences and thereby to a possible exchange between decision makers of various preferences. Risk is then managed by aggregating individual risks and sharing the global (and variance reduced) risks. Insurance firms have recognized the opportunities of such differences and have, therefore, capitalized on it by pooling highly variable risks and redistributing them, thereby using the “willingness to pay to avoid losses ” of insured. It is because of such attitudes and broadly differing individual preferences towards risk avoidance that markets for fire and theft insurance, as well as sickness, unemployment, accident insurance, etc., have come to be as lucrative as they are today. It is because of persons or firms’ desires to avoid too great a loss (even with small probabilities) which would have to be borne alone, that markets for reinsurance (i.e., sub-selling portions of insurance contracts) and mutual protection insurance (based on the pooling of risks, government support to certain activities) have also come into being. In the last ten years, financial cotracts have been applied to price insurance contracts. It is also for this reason that in the mid-nineties I stopped to work on Intertemporal model of mutual insurance (when I was perhaps one of the first to recognize and use such models). However, market incompleteness, a revival of actuarial and insurance research due to the prospect of pensions funds privatization, have raised again the interest in this area—an interest which can be translated into funded research and course development.
Finance and financial markets require willing risk averters and risk takers to exchange and thereby transfer risk from parties to parties. Insurance however, emphasizes a different (albeit complementary) approach based on aggregation and redistribution of risk through intermediaries. The meeting of finance and insurance has contributed to a “market approach to insurance” while transforming insurance firms to market intermediaries. This has many implications that opens up many avenues for future research. Explicitly, we may be in a better position to manage and share risks globally, it may contribute to a greater ability for individuals to deal individually and collectively, with risk and thus contribute to the pricing and optimization of risk distribution. In some cases, this risk shifting is not preferable due to the effects of moral hazard, adverse selection and generally information asymmetry. To compensate for these effects however, a number of actions are taken such as monitoring and using incentive contracts to motivate and alter the behavior of the parties to the contract so that they will comply to the terms of the contract whether willingly or not. This facet of risk management is of special interest to the Chair’s research efforts.
The integration of insurance practice with financial management is an important area for both technology and financial services.
Empirical evidence has shown that financial time series are not always "well behaved". They may have an unpredictable variance, underscoring departures from the "random walk hypothesis" which is essential to define market completeness. These effects have been recognized and have been the subject of considerable research under the heading of ARCH and GARCH related models focusing on the estimation of an underlying process variance. Such research has been recognized by awarding to Engle's the Nobel Prize. My research has sought to complement such an approach by using time series range samples as an essential statistics in stochastic processes to detect outliers and to control volatility. In this research I focus attention to the use of the inverse range process for which specific and statistical properties can be defined (extensive research along these lines have been published by Vallois and myself—see CV). In this sense, the intent of this research is to use the inverse range process as a statistic for volatility (variance) and the detection of chaotic processes (of importance not only to finance).
Problems related to volatility (variance) estimation are particularly important in finance however. For example, an investor—a buyer of options, may have only a probabilistic assessment of the underlying stock volatility, which is essential for option's pricing. Detecting the “stochasticity” of volatility may be indicative and equivalent to specifying when does a complete market become incomplete. Similarly, in process control using charts for determining drifts in volatility, the process range might be used to test validity of a given set of control barriers. Further research is needed however to highlight the usefulness and the applicability of such an analysis to important decision making problems with a-priori unknown or stochastic volatility.
Bonds are binding obligations by the bond issuer to pay the bond-holder (buyer) certain amounts of money at given dates. Some bonds may be subject to default and to various sources of uncertainties, The rating of bonds provided by firms such as Standard and Poor, Moody’s etc. provide an estimate of a bond quality. The literature on such problems is extremely large based on two classes of models, structural and endogenous models. Some bonds may default or delay on the coupon payout, default at redemption (wholly or partly). The valuation and analysis of default bonds, based on the rating matrix, is due to Jarrow and Turnbull as well as Jarrow, Lando and Turnbull. Their essential contribution consisted on the one hand in formulating the default prone rated bond valuation problem and in the construction of a risk neutral framework based on the forward rate. My research considers problems in a discrete time framework and using the term structure of risk free rates to calculate the ratings discounts. Such an analysis is theoretically challenging and computationally difficult. Preliminary analyses can be found in Tapiero's book (Wiley, 2004, March). Extensions of such an approach to semi-markov rated bond models provides an opportunity to include a greater number of factors that are affecting the price of rated bonds. Following my involvement as a member of the academic board of Standard and Poor in Europe, I have become aware that rating and rating valuation is a field which requires much more research to better differentiate firms risk rating. Further, the problems of Banks in granting credit has also induced me to study in greater depth their techniques for credit scoring.
Risk measurements and controls are of critical importance for managing financial risks. In the last few years extensive use is made in practice of a measure of risk exposure called VaR or Value at Risk. The extensive literature on this topic attests to the growth and the importance of such an approach. VaR seeks to measure the expected loss from an adverse market movement with specified probability over a period of time. Thus, to compensate the market risk exposure, financial institutions may set aside a certain amount of capital so that the probability that the institution will not survive adverse market conditions remains very small.
My research in this area consists of two essential directions. A first seeks to adapt the financial risk approach to operational problems and thereby contribute to the meeting of minds between operational and financial risk management. I have a number of papers along these lines that have been published but I assume that there will be few more based on potential joint research or theses I may supervise in the future in these areas.
On purely theoretical grounds, I am studying a particular aspect of risk measurement: “Volatility at Risk” based on the inverse range process which I call “Range Volatility at Risk” or “RVaR”. Such a statistic will complete the VaR approach by providing an expression for the portfolio or assets under VaR control by focusing both on the gain-loss process the portfolio volatility. The RVaR, defined in the spirit of VaR will specify the risk (volatility) a portfolio can predictably sustain over a given period of time, by a range domain variation. In other words, given a portfolio predictable returns’ distribution we specify the risk and the time over which the portfolio range of values (the portfolio amplitude) will be maintained.
I have also added an inter-temporal dimension to VaR and RVaR analysis by considering as well a whole range of parameters which can be used in managing the risk exposure of a portfolio. Such an approach maintains a portfolio wealth state fluctuations within a given range-amplitude of RVaR over an appropriately specified amount of time TRVaR and with probability PVaR. The Volatility at Risk of such a portfolio is then managed by tracking over time the evolution of the portfolio fluctuations (his range). If the range varies “too much”, “growing too fast” and thereby exceeding the RVaR prior to a time consistent with the “volatility risk” specifications, then some form of intervention (buy-sell stocks or bonds, options and/or future contracts) may be needed to adjust the portfolio so that it remains consistent with the risk parameters specifications. Similarly, a portfolio may be selected combining risk free and risky assets to meet an RvaR (volatility) risk specification. Preliminary mathematical analyses of these problems can be found as well in my books (Applied Stochastic Models and Control in Finance and Insurance, Kluwer, 1998 and Financial Risk Management: mathematical and Computational Concepts, Wiley, 2004 and in some of my working papers and research submitted for publication.
Externalities are not an exception but the rule! Most business and economic activities have derived external effects not accounted for (in a traditional accounting sense) and priced by the market. A driver emits gases when he drives and it is the collective which is taxed by assuming the deterioration in air quality. Externality, therefore, expresses both a risk—with positive or negative consequences, usually sustained by a collective (a society) and a breakdown of the market mechanism which does not price these effects into the process of rational decision making. Inversely, consumers may behave in a manner that they can affect society at large without having to sustain the consequences of their actions. When these effects are important, we may call them “terrorists”, “polluters” etc. Firms, and in particular providers may be directly targeted in this manner with the cost sustained by both the firms and the public at large.
Risk externalities, upstream and downstream motivated, contribute therefore to the risk environment a society and firms are subjected to. These risk facets are assuming a growing importance and it is necessary and useful that they be subject to greater research—in insurance, in finance and in mathematics and financial econometrics. In other words, this requires that we develop the appropriate tools to assess their effects on financial performance and the risk valuation of their potential impact. Risk management involves an important set of tools that can convey and value the adverse consequences of intended actions, but they have mostly failed in providing the required means of analysis and management in dealing with risk externalities. Some experience has been acquired in managing environmental risks, but it is mostly unsatisfactory.
My research in this area attempts to develop a coherent and a holistic framework in dealing with problems of risk externality and their effects on insurance and financial markets and in a better valuation of operational and environmental risks. The task of such an endeavor is immense involving specific and strategic issues which are studied in a coherent framework summarized in a book project I intend to pursue (a continuation of my recent Financial Risk Management: Mathematical and Computational Concepts Wiley 2004).
It is vital to adhere to the concept of sustainable development, taking into account the repercussions originating from production, consumption and various socio-economic factors. Research on new industrial technologies, methodologies and risk prevention aiming, not only at a sustainable and even better environment, but also at sustainable competitiveness, represents a key issue.
In contrast, the specific and derived effects of SD (and vice versa) have received little attention. While some attention has been diverted to the externalities of the industrial process (such as the environmental impact, hazard risks of various sorts and their like), the impact of SD on industrial policy and the economic decision making process has yet to be addressed in a systemic manner, providing a long run, self perpetuating, equitable and environmental friendly development. SD awareness has raised both opportunities and risks to industrial enterprises. Related research topics are numerous. Some of which I am pursuing but others are likely to be motivated by my interaction with environmental researchers and economists. In particular, the following topics summarizes essential problems to reckon with:
Investments in infrastructure are means applied to some end. It is as a result, a derivative, whose value is derived by others who use it (just as options derive their value from an underlying asset). For example, building a highway, building a better educational system etc. contribute to individuals welfare and thereby to society. It is a widely applied in industry, in services, in the military and in many areas of business, information and technology that profit from infrastructure investments. A “financial market approach” to infrastructure investments can enrich both finance and social investments, providing an opportunity to turn to financial markets in order to financial social investments that governmental institutions cannot or will not assume.
This research considers an environmental game based on a queue-stochastic framework I have devised, some of which has been published. Such an approach makes it possible to internalize the pollution effects of firms economic activities and thereby can be used for pricing the firms’ risk externalities. Such an approach in this context is to my knowledge an innovation providing many opportunities for theoretical and applied research in risk externalities, financial economics and environmental problems (see my recently published papers).
The problem I consider involves an environmental agency-- "the regulator" and potentially "polluting firms", each with varied motivations and thereby leading to a game played between the agency and the firms. For our purposes and for simplification we assume that the firm uses a pollution technology determined by the quantity of products (or employment) it produces as well as by the preventive and pollution abatement technology it applies to its industrial and production processes. The firm motivation will be to maximize average profits once it takes into account both the payoff resulting from its economic activity and the costs associated to pollution (as well as the penalties incurred when the polluting firm is detected and penalized by the environmental agency). Pollution risks, measured by their consequences are, however, a function of the regulators controls. Thee results in a random payoff game where the firm's policies consist in selecting an appropriate level of industrial activity (investment, employment), investing in preventive measures as well as controlling ex-post pollution events. The environmental agency however will seek to optimize the environmental quality by expending environmental control efforts which are subject to numerous constraints (such as budget, employment requirements, financial sustainability of the firm and their like).
Specifically, the problems that both the firm and the regulator are faced with are then two-fold: (1) Given a polluting technology and a shared penalty cost for polluting event, what are the control effort to exercise by the firm and what control and preventive efforts to exercise by the firm and (2) What are the effects of the technology choice and penalty-cost sharing parameters on the firm and society's payoffs.
This research project should therefore lead to theoretical insights based on risk and gaming problems and of course using national data regarding economic development and environmental impact and how much are people willing to pay for a clean environment. And perhaps find some mechanism to finance environment friendly industrial activities.
Preliminary research has been published, but a number of extensions could be used as a foundation for students’ theses.
The purpose of this research project is to look for an alternative to solutions based on Nash Equilibria applied in many problems which is in my view over conservative. For example, I consider notions of "satisficing" games. The concept "satisficing solution" to a game is based on two essential presumptions. First, that game participants have objectives they want to meet (constraints) absolutely or in a probabilistic manner, by specifying the risks they are willing to sustain and associated to each potential strategy. Second, it presumes that in the absence of a well defined objective (except of course, those specified through an appropriate set of constraints), a solution is defined by strategies that assumes the least regarding players motivation. In other words, it applies the principle of Laplace of Insufficient Reason to the game solution. This results in a solution which is less conservative than Nash's solution for nonzero sum games. In this vein, environmental games are not conceived as mathematical games of pure conflict but rather games with nuances of potential collaboration, occurring in a probabilistic manner to provide a "satisficing solution"--meaning that agents will not act purposefully as if they were in conflict. For practical purposes and in order to calculate a "satisficing" random strategy solution for each of the players we will apply for example a Maximum Relative Entropy objective, for both agents. The problems we thus consider involve both the firm and the environmental regulator. In an applied context, they raise two issues: (1) Given a polluting technology and a shared penalty cost for polluting events, what are the control efforts to exercise by the firm and what control and preventive efforts to exercise by the firm and (2) What are the effects of the technology choice and penalty-cost sharing parameters on the firm and on the regulating environmental agency's payoffs. The solutions we might consider are based essentially on constrained random payoff games for which initial result are available in my recently published papers (see CV and publications in 2005).
Finally, I have also contributed over the years to numerous ideas and papers to deal with Operational Risks, Supply Chains Risk Management, Industrial and Technology Risks (see the CV) and hopefully will continue to do so but preferably by interacting with the Professors and students at NYU-Poly (in particular those involved in the Technology programs such as Professor Mel orwhich, Professor Bharat, Professor Bleicherman and persons who would express such an interest. These research include among others the control of quality in Queue Like Flexible Systems and the control of delivery contracts in supply chains (see papers with Dyane Reyniers) Summarily, my efforts in these areas in the past have focused on quality, Logistic, Transport, Services, and Industrial Risk Management as well as Supply Chain contracts and their management. OperationsRisk management policies in industrial as well as in financial services may imply organizing the supply chain, managing deliveries effectively, better forecasting methods and appropriate distributions describing parts usage, life and reliabilities. In addition, emergency needs, large demand variability, supply constraints—in particular regarding substantial supply delays (and probably uncertainty in supply delays) etc. requiring a large mix of equipment, repair policies and depots, maintenance and replacement policies, may be some of the factors to reckon with in designing a logistic and industrial risk management policy seeking to save money.
Similarly, buffer stocks are needed to manage risks associated to demands that are not met, to build the capacity to meet demands, to smooth productions processes, resumed by a desire to save money or reduce risks, i.e. reduce the costs associated with adverse consequences. Stocks or inventory policies, when they are properly applied can increase efficiency and reduce industrial and logistic-services risks. The construction of such policies in retail distribution and their economic-financial valuation are important research problems to reckon with and to which I have already contributed extensively. By the same token, there is an abundance of research topics in the management of risk in Supply Chains. Some of the topics may include:
Such a research agenda can be realized only through extensive and intensive cooperation with both students and faculty at Polytechnic Institute of NYU.