Satisficing measures for analysis of risky positions

David B. Brown (dbbrownduke.edu)
Melvyn Sim (dscsimmnus.edu.sg)

Abstract: In this work we consider a class of measures for evaluating the quality of financial positions with uncertain payoffs based on their ability to achieve desired financial goals. In the spirit of Simon (1959), we call these measures satisficing measures and show that they are dual to classes of corresponding risk measures. This approach has the advantage that aspiration levels (either competing benchmarks or fixed targets) are often natural for investors to specify, as opposed to the risk-tolerance type parameters, which can be difficult to understand intuitively and hard to appropriately specify, that are necessary for many other approaches (risk measures, utility functions, etc.). Moreover, we explore a class of satisficing measures that have quasi-concavity properties which ensure that they appropriately reward for diversification. This further implies that optimization of these measures can be approached using computationally tractable tools from convex optimization, in contrast to the difficult, combinatorial problems that plague optimization of value-at-risk and related measures. Finally, when our satisficing measures have a particular scale invariance property, we are able to represent them in terms of expected value over an ambiguous probability distribution; additionally, these satisficing measures have a separation property which allows us to compute a single tangent portfolio regardless of the investor's desired expected return.

Keywords: satisficing, aspiration levels, targets, risk measures, coherent risk measures, convex risk measures, portfolio optimization

Category 1: Applications -- OR and Management Sciences (Finance and Economics )

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Entry Submitted: 06/12/2007
Entry Accepted: 06/13/2007
Entry Last Modified: 02/09/2008

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