Nikolaus Schweizer

Optimal Revelation of Life-Changing Information

Information about the future may be instrumentally useful, yet scary. For example, many patients shy away from precise genetic tests about their dispositions for severe diseases. They are afraid that a bad test result could render them desperate due to anticipatory feelings. We show that partially revealing tests are typically optimal when anticipatory utility interacts with an instrumental need for information. The same result emerges when patients rely on probability weighting. Optimal tests provide only two signals, which renders them easily implementable. While the good signal is typically precise, the bad one remains coarse. This way, patients have a substantial chance to learn that they are free of the genetic risk in question. Yet even if the test outcome is bad, they do not end in a situation of no hope.

Pathwise Dynamic Programming

We present a novel method for deriving tight Monte Carlo confidence intervals for solutions of stochastic dynamic programming equations. Taking some approximate solution to the equation as an input, we construct pathwise recursions with a known bias. Suitably coupling the recursions for lower and upper bounds ensures that the method is applicable even when the dynamic program does not satisfy a comparison principle. We apply our method to three nonlinear option pricing problems, pricing under bilateral counterparty risk, under uncertain volatility, and under negotiated collateralization.

Information Nudges and Self Control

We study the optimal design of information nudges for present-biased consumers who have to make sequential consumption decisions without exact prior knowledge of their long-term consequences. For arbitrary distributions of risk, there exists a consumer-optimal information nudge that is of cutoff type, recommending consumption or abstinence according to the magnitude of the risk. Under a stronger bias for the present, the target group receiving a credible signal to abstain must be tightened. We compare this nudge with those favored by a health authority or a lobbyist. When some consumers are more strongly present-biased than others, a traffic-light nudge is optimal.

Iterative Improvement of Lower and Upper Bounds for Backward SDEs

We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semilinear partial differential equations. Solving such dynamic programs numerically requires the approximation of nested conditional expectations, i.e., iterated integrals of previous approximations. Our approach allows us to compute and iteratively improve upper and lower bounds on the true solution, starting from an arbitrary and possibly crude input approximation. We demonstrate the benefits of our approach in a high-dimensional financial application.

Revenues and welfare in auctions with information release

Auctions are the allocation-mechanisms of choice whenever goods and information in markets are scarce. Therefore, understanding how information affects welfare and revenues in these markets is of fundamental interest. We introduce new statistical concepts, k- and k-m-dispersion, for understanding the impact of information release. With these tools, we study the comparative statics of welfare versus revenues for auctions with one or more objects and varying numbers of bidders. Depending on which parts of a distribution of valuations are most affected by information release, welfare may react more strongly than revenues, or vice versa.