BAYES DECISION MAKING
2.2 BAYES DECISION MAKING
The basic elements of Bayes rational decision making involve behaviours includ- ing:
(1) A decision to be taken from a set of known alternatives. (2) Uncertainty defined in terms of events with associated known (subjective)
probabilities. (3) Conditional consequences resulting from the selection of a decision and the
occurrence of a specific event (once uncertainty, ex-post, is resolved). (4) A preference over consequences, i.e. there is a well-specified preference function or procedure for selecting a specific alternative among a set of given alternatives.
An indifferent decision maker does not really have a problem. A problem arises when certain outcomes are preferred over others (such as making more money over less) and when preferences are sensitive to the risks associated with such outcomes. What are these preferences? There are several possibilities, each based on the information available – what is known and not known and how we balance the two and our attitude toward risk (or put simply, how we relate to the probabili- ties of uncertain outcomes, their magnitude and their adverse consequences). For these reasons, risk management in practice is very important, impacting events’ desirability and their probabilities. There are many ways to do so, as we shall see below.
BAYES DECISION MAKING
2.2.1 Risk management
Risk results from the direct and indirect adverse consequences of outcomes and events that were not accounted for, for which we are ill-prepared, and which effects individuals, firms, financial markets and society at large. It can result from many reasons, both internally induced and occurring externally. In the for- mer case, consequences are the result of failures or misjudgements, while, in the latter, these are the results of uncontrollable events or events we cannot pre- vent. As a result, a definition of risk involves (i) consequences, (ii) their prob- abilities and their distribution, (iii) individual preferences and (iv) collective, market and sharing effects. These are relevant to a broad number of fields as well, each providing an approach to measurement, valuation and minimization 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.
Risk management is broadly applied in finance. Financial economics, for ex- ample, deals intensively with hedging problems in to order eliminate risks in a particular portfolio through a trade or a series of trades, or through contractual agreements reached to share and induce a reduction of risk by the parties in- volved. Risk management consists then in using financial instruments to negate the effects of risk. It might mean a judicious use of options, contracts, swaps, insurance contracts, investment portfolio design etc. so that risks are brought to bearable economic costs. These tools cost money and, therefore, risk management requires a careful balancing of the numerous factors that affect risk, the costs of applying these tools and a specification of (or constraints on) tolerable risks an economic optimization will be required to fulfil. For example, options require that a premium be paid to limit the size of losses just as the insured are required to pay a premium to buy an insurance contract to protect them in case an adverse event occurs (accidents, thefts, diseases, unemployment, fire, etc.). By the same token, ‘value at risk’ (see Chapter 10) is based on a quantile risk constraint, which provides an estimate of risk exposure. Each profession devises the tools it can apply to manage the more important risks to which it is subjected.
The definition of risk, risk measurement and risk management are closely related, one feeding the other to determine the proper/optimal levels of risk. In this process a number of tools are used based on:
r ex-ante risk management, r ex-post risk management and r robustness.
Ex-ante risk minimization involves the application of preventive controls; pre- ventive actions of various forms; information seeking, statistical analysis and forecasting; design for reliability; insurance and financial risk management etc. Ex-post risk minimization involves by contrast control audits, the design of op- tional, flexible-reactive schemes that can deal with problems once they have occurred and limit their consequences. Robust design, unlike ex-ante and ex-post risk minimization, seeks to reduce risk by rendering a process insensitive to its
24 MAKING ECONOMIC DECISIONS UNDER UNCERTAINTY
adverse consequences. Thus, risk management consists of altering the states a system many reach in a desirable manner (financial, portfolio, cash flow etc.), and their probabilities or reducing their consequences to planned or economi- cally tolerable levels . There are many ways to do so, however, each profession devises the tools it can apply or create a market for. For example, insurance firms use reinsurance to share the risks insured while financial managers use derivative products to contain unsustainable risks.
Risk management tools are applied in insurance and finance in many ways. Control seeks to ascertain that ‘what is intended occurs’. It is exercised in a number of ways rectifying decisions taken after a nonconforming event or problem has been detected. For example, auditing a trader, controlling a portfolio performance over time etc. are such instances. The disappearance of $750 million at AIB (Allied Irish Bank) in 2002 for example, accelerated implementation of control procedures within the bank and its overseas traders.
Insurance is a medium or a market for risk, substituting payments now for po- tential damages (reimbursed) later. The size of such payments and the potential damages that may occur with various probabilities, can lead to widely dis- tributed market preferences and thereby to a possible exchange between decision- makers of various preferences. Insurance firms have recognized the opportuni- ties of such differences and have, therefore, provided mechanisms for pooling, redistributing and capitalizing on the ‘willingness to pay to avoid losses’. It is because of such attitudes, combined with goals of personal gain, social welfare and economic efficiency, that markets for fire and theft insurance, as well as sickness, unemployment, accident insurance, etc., have come to be as impor- tant as they are today. It is because of persons’ or institutions’ 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 con- tracts) and mutual protection insurance (based on the pooling of risks) have also come into being. Today, risk management in insurance has evolved and is much more in tune with the valuation of insurance risks by financial markets. Under- standing the treatment of risk by financial markets; the ‘law of the single price’ (which we shall consider below); risk diversification (when is is possible) and risk transfer techniques using a broad set of financial instruments currently used and traded in financial markets; the valuation of risk premiums and the estimation of yield curves (see also Chapter 8); mastering financial statistical and simula- tion techniques; and finally devising applicable risk metrics and measurement approaches for insurance firms – all have become essential for insurance risk management.
While insurance is a passive form of risk management, based on exchange mechanisms only (or, equivalently, ‘passing the buck’ to some willing agent), loss prevention and technological innovations are active means of managing risks. Loss prevention is a means of altering the probabilities and the states of undesir- able, damaging states. For example, maintaining one’s own car properly is a form of loss prevention seeking to alter the chances of having an accident. Similarly, driving carefully, locking one’s own home effectively, installing fire alarms, etc. are all forms of loss prevention. Of course, insurance and loss prevention are, in
25 fact, two means to the similar end of risk protection. Car insurance rates tend,
BAYES DECISION MAKING
for example, to be linked to a person’s past driving record. Certain clients (or areas) might be classified as ‘high risk clients’, required to pay higher insurance fees. Inequities in insurance rates will occur, however, because of an imperfect knowledge of the probabilities of damages and because of the imperfect distribu- tion of information between the insured and insurers. Thus, situations may occur where persons might be ‘over-insured’ and have no motivation to engage in loss prevention. Such outcomes, known as ‘moral hazard’ (to be seen in greater detail in Chapter 3), counter the basic purposes of insurance. It is a phenomenon that can recur in a society in widely different forms, however. Over-insuring unem- ployment may stimulate persons not to work, while under-insuring may create uncalled-for social inequities. Low car insurance rates (for some) can lead to reckless driving, leading to unnecessary damages inflicted on others, on public properties, etc. Risk management, therefore, seeks to ensure that risk protection does not become necessarily a reason for not working. More generally, risk man- agement in finance considers both risks to the investor and their implications for returns, ‘pricing one at the expense of the other’. In this sense, finance, has gone one step further in using the market to price the cost an investor is willing to sustain to prevent the losses he may incur. Financial instruments such as op- tions provide a typical example. For this reason, given the importance of financial markets, many insurance contracts have to be reassessed and valued using basic financial instruments.
Technological innovation means that the structural process through which a given set of inputs is transformed into an output is altered. For example, building
a new six-lane highway can be viewed as a way for the public to change the ‘production-efficiency function’ of transport servicing. Environmental protection regulation and legal procedures have, in fact, had a technological impact by requiring firms to change the way in which they convert inputs into outputs, by considering as well the treatment of refuse. Further, pollution permits have induced companies to reduce their pollution emissions in a given by-product and sell excess pollution to less efficient firms.
Forecasting, learning, information and its distribution is also an essential in- gredient of risk management. Banks learn every day how to price and manage risk better, yet they are still acutely aware of their limits when dealing with complex portfolios of structured products. Further, most non-linear risk measurement and assessment are still ‘terra incognita’ asymmetries. Information between insured and insurers, between buyers and sellers, etc., are creating a wide range of op- portunities and problems that provide great challenges to risk managers and, for some, ‘computational headaches’ because they may be difficult to value. These problems are assuming added importance in the age of internet access for all and in the age of ‘total information accessibility’. Do insurance and credit card companies have access to your confidential files? Is information distribution now swiftly moving in their favour? These are issues creating ‘market inefficiencies’ as we shall see in far greater detail in Chapter 9.
Robustness expresses the insensitivity of a process to the randomness of pa- rameters (or mis-specification of the model) on which it is based. The search for
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robust solutions and models has led to many approaches and techniques of opti- mization. Techniques such as VaR (Value at Risk), scenario optimization, regret and ex-post optimization, min-max objectives and the like (see Chapter 10) seek to construct robust systems. These are important tools for risk management; we shall study them here at length. They may augment the useful life of a portfolio strategy as well as provide a better guarantee that ‘what is intended will likely occur’, even though, as reality unfolds over time, working assumptions made when the model was initially constructed turn out to be quite different.
Traditional decision problems presume that there are homogeneous decision makers, deciding as well what information is relevant. In reality, decision makers may be heterogeneous, exhibiting broadly varying preferences, varied access to information and a varied ability to analyse (forecast) and compute it. In this envi- ronment, decision-making becomes an extremely difficult process to understand and decisions become difficult to make. For example, when there are few major traders, the apprehension of each other’s trades induces an endogenous uncer- tainty, resulting from a mutual assessment of intentions, knowledge, knowhow etc. A game may set in based on an appreciation of strategic motivations and intentions. This may result in the temptation to collude and resort to opportunistic behaviour.