If f is twice continuously differentiable, then supermodularity is equivalent to the condition . The concept of supermodularity is used in the social sciences to analyze how one agent's decision affects the incentives of others. Following the terminology of Bulow, Geanakoplosand Klemperereconomists call this situation strategic complementaritybecause players' strategies are complements to each other. For example, Bulow et al. When an increase in output by one firm raises the marginal revenues of the other firms, production decisions are strategic complements.
When an increase in output by one firm lowers the marginal revenues of the other firms, production decisions are strategic substitutes. A supermodular utility function is often related to complementary goods. However, this view is disputed. Supermodularity and submodularity are also defined for functions defined over subsets of a larger set. Intuitively, a submodular function over the subsets demonstrates "diminishing returns". There are specialized techniques for optimizing submodular functions.
Let S be a finite set. For supermodularity, the inequality is reversed. From Wikipedia, the free encyclopedia. Redirected from Increasing differences. See Milgrom, Paul; Roberts, John Journal of Political Economy. Quarterly Journal of Economics. Journal of Economic Theory. Categories : Order theory Optimization of ordered sets Generalized convexity Supermodular functions.
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FRED data. Notes on supermodularity and increasing differences in expected utility. Many choice-theoretic and game-theoretic applications in Economics invoke some form of supermodularity or increasing differences for objective functions defined on lattices. These notes provide axiomatic foundations for these properties on expected-utility representations of preferences over lotteries.
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Notes on supermodularity and increasing differences in expected utility
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If the futures price gets out of whack, they cannot hedge an index futures purchase or sale through an offsetting sale or purchase of the underlying stocks. But other market participants are still active. Index Futures Predict the Opening Direction Suppose good news comes out abroad overnight - the ECB cuts interest rates, or China reports stronger than expected growth in GDP.
The local equity markets will probably rise, and investors may anticipate a stronger U. If they buy index futures, the price will go up. And with index arbitrageurs on the sidelines until the U.
As soon as New York opens, though, the index arbitrageurs will execute whatever trades are needed to bring the index futures price back in line - in this example, by buying the component stocks and selling index futures. Investors cannot just check whether the futures price is above or below its closing value on the previous day, though. The dividend adjustments to index futures fair value change overnight (they are constant during each day), and the indicated market direction depends on the price of index futures relative to fair value regardless of the preceding close.
On a day when several big index constituents go ex-dividend, index futures may trade above the prior close but still imply a lower opening. Trading is typically volatile at the opening, which accounts for a disproportionate amount of total trading volume. If an institutional investor weighs in with a large buy or sell program in multiple stocks, the market impact can overwhelm whatever price movement the index futures indicate.
Institutional traders do watch futures prices, of course, but the bigger the orders they have to execute, the less important the index futures direction signal becomes. Late openings can also disrupt index arbitrage activity. Although the market opens at 9:30am, not every stock starts to trade at once.
The opening price is set through an auction procedure, and if the bids and offers do not overlap, the stock remains closed until matching orders come in. The longer index arbitrageurs stay on the sidelines, the greater the chances that other market activity will negate the index futures direction signal.
The Bottom Line If the futures price suggests the market will rise on the opening, investors who wish to sell that day may want to wait until after the market opens before entering their order, or set a higher price limit.
Buyers may want to hold off when index futures predict a lower opening, too. Investors can monitor futures prices and fair values on websites like CNBC or CNN Money, both of which also show pre-market indications for individual stocks (a less reliable indicator due to poor liquidity). Here's help in making the decision.
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