Risk-taking-neutral background risk
2011-05-31 17:00 - 18:30 (Europe/London) | United Kingdom
Harris Schlesinger
Bio sketch: Dr. Schlesinger is past president of both the American Risk and Insurance Association and the European Group of Risk and Insurance Economists. He has held visiting appointments in Belgium, France, Germany and Switzerland. He was the founding editor of the Geneva Papers in Risk and Insurance Theory and currently is an associate editor for five academic journals. His research papers have won several awards, including the JRI Best Article Award (5 times), the Decision Analysis Best Paper Award from INFORMS, and the Kulp-Wright Book Award. He received the 2007 Burnum Distinguished Faculty Award at UA and he received the Minerva Award as outstanding alumnus from his undergraduate college. Dr. Schlesinger has been a Research Fellow for the CPCU Harry J. Loman Foundation, the National Science Foundation, the Science Center in Berlin (Germany), the Center for Economic Studies (Germany) and the Center for Intercollegiate Studies in Management Science (Belgium). He is currently a Senior Research Fellow with CESifo, a European-based economic policy organization. He has published articles in more than two dozen journals, including the American Economic Review, Journal of Finance, Econometrica, Quarterly Journal of Economics and Journal of Political Economy.
Abstract:This paper examines how decision making under uncertainty is affected by the presence of a background risk. By background risk, we refer to a risk for which there is no market for trading or hedging. In particular, we construct a class of background risks that we label as risk-taking-neutral (RTN). These background risks have the property that they will not alter the choice decisions made with respect to another risk.
As a concrete example, consider buying insurance for a loss exposure. The effects of various background risks on the purchase of insurance has long been of interest. See, for example Doherty and Schlesinger (1983) and Dana and Scarsini (2007). Or consider the similar problem of choosing how to split investment between a risky and a riskless asset. The effects of an independent background risk has been examined in depth by Gollier and Pratt (1996), Campbell and Viceira (2007), and others.
The RTN background risks that we construct can provide a benchmark. Essentially, the solution to all of these types of insurance and investment decisions equates marginal-utility costs to marginal-utility benefits. Our RTN background risk affects marginal utility proportionately at all levels. Thus, if marginal utility is say 10% higher at all wealth levels, benefits and costs will be equal at the same optimal level as without the background risk. In many situations, a particular background risk that is faced by an investor can be
We consider both the investment problem and the insurance problem as our applications. We apply our RTN methodology to three particular examples of background risks. First, we consider an independent background risk, as examined by Gollier and Pratt (1996), and show how our methodology can be used to derive some of their results. Second, we consider the case of a flat tax rate and show that either a wealth tax or an income tax at a flat rate will cause investment in the risky asset to increase, in the standard portfolio problem. Third, we set-up a model with ambiguity (also known as “parameter uncertainty”) and show how it can be modeled using RTN background risk.
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